"Sometimes a dark spot or a mole enhances the beauty."
Our Constitution as the longest written constitution in the world is home to a lot of oddities and place overs and from the 70 odd years that the constitution has been in force. A lot of unnecessary and bewildering provisions have found their way to the constitution over the years. There are a lot of provisions that came into place as a result of the push and pull between the judiciary and the legislature, but also between the various Governments.
One such oddity is Article 361A that protects newspapers and media more broadly from prosecution for reporting on the proceedings in the house. This came about as a result of the darkest phase of the Indian Republic.
The Emergency (1975-77) was a two year period of immense turmoil as the Government of India led by Indira Gandhi invoked Article 352 of the constitution after a period of political and legal disputes over her election. Those two years are the darkest period of the Indian Republic as Opposition leaders were arrested en masse and activity by Opposition Political Parties were limited or close to non existent, with those not arrested in hiding.
Holding a majority in both the Lok Sabha and Rajya Sabha (and the Emergency providing powers additional powers to the Parliament), Indira's writ ran completely unopposed. After having invoked emergency, substantial and significant changes that scarred the constitutional text forever were made. Along with this, a bunch of statutes were repealed or replaced. One of the statutes that were repealed was The Parliamentary Proceedings (Protection of Publication) Act, 1956.
The Legislation had come about as a result of the efforts of Feroze Gandhi, who introduced a private member's bill giving protection for newspapers from prosecution for publishing the proceedings of both Central and State Legislatives assemblies that are "substantially true" and not "made with malice". The Bill was narrowed in the house to apply to only to Parliamentary procedure as it was not empowered to legislate on State Legislatures, but was passed by both Houses. Till date, it remains one of few legislations introduced by a private member to become law.
But why was such a bill necessary? The answer lies in Parliamentary privileges under Article 105 that essentially protect the Free Speech of every member of the house among other things.
These powers, being of the widest ones, is only limited by procedural rules and Article 121 that prevents members form discussing the conduct of any High Court or Supreme Court Judge. Thus, a legislator is protected from potentially defamatory statements or other criminal prosecution for the Statements made in due course by the Parliament.  The reportage of the proceedings in the house, without fear of prosecution for publishing the proceedings was what the 1956 Act achieved. This, as noted during the debate on the Bill in 1956 was cardinal to the idea of privileging members themselves: without dissemination of the information that members could provide under privilege, it was not as useful.
During emergency, the remaining members of the opposition in the Parliament sought to bring attention to the various excesses and injustices that were being conducted during the period in the House. The reporting of the same was protected by the 1956 Act. To circumvent this, an ordinance was issued on 08th December, 1975 to repeal this act as well as the Press Council Act, along with the promulgation of the Prevention of Publication of Objectionable Matter Act, which imposed a full censorship regime on the media.  The ordinance was approved without much hassle in the Parliament, bringing about the end of protection for newspapers.
After Emergency ended, the 1977 elections returned the Janata party that had more or less united all of the opposition parties. The Janata Government set out to repeal the changes imposed during the emergency. Within a few days of the election, L.K. Advani, the then Minister of Information and Broadcasting re-introduced the text of the 1956 Act verbatim into the house as the Parliamentary Proceedings (Protection of Publication) Bill, 1977.
In fact, the Janata Party eventually got the 44th Constitutional Amendment passed, which undid some of the damage that the 42nd amendment did to the Constitution.  The 44th Amendment had the Article 361A, which extended the protection for reporting the proceedings to newspapers for both the Parliament and State Legislature. 
In tracing out the lineage of this single Article, one can see the political pressures and equations that motivated the members of Parliament at various times. The total and absolute nature of the restrictions imposed during The Emergency can be understood from the repeal and removal of an almost inconsequential protection afforded to media was taken away in an effort to fully repress any opposition. The constitutional text is a product of the political and legal history, and this Article is another speck that came out as a result of the Emergency.
Addendum: A fascinating side tale when discussing this matter is that case of C.K. Daphtary v. O.P. Gupta (1970). The case involved a contempt of court action against a bureaucrat who circulated defamatory statements about Retired Chief Justic J.C. Shah (yes, of Shah Commission fame). O.P. Gupta held a grudge against Justice Shah for supposedly insulting him during a court proceeding. Eventually 199 Lok Sabha MPs, who sought to introduce an impeachment motion against Shah based on this. However, the speaker turned down this motion. Subsequently the Supreme Court prosecuted and punished Gupta for contempt of court. He had argues that his pamphlets were protected under the 1956 Act, but the court decided that the publication of the pamphlet was not a newspaper and was not per se regarding a proceeding in the Parliament. The court punished him with a simple imprisonment of two months.
Report on the 1956 Bill Tabled on May 1st, 1956: lsd_01_12_01-05-1956.pdf (eparlib.nic.in)
Discussion on the Bill in the Lok Sabha on 4th May, 1956: lsd_01_12_04-05-1956.pdf (eparlib.nic.in)
Discussion on the Bill in the Rajya Sabha on 11th May, 1956: Microsoft Word - 13_15_11051956.doc (rsdebate.nic.in)
Repeal of 1956 Act Ordinance Tabled on 05th January 1976: lsd_05_15_05-01-1976.pdf (eparlib.nic.in)
Discussion on the 1976 Repeal Act in Lok Sabha on 28th January 1976: lsd_05_15_28-01-1976.pdf (eparlib.nic.in)
Bill introduced in the Lok Sabha on 4th April, 1977: lsd_06_01_04_04_1977.pdf (eparlib.nic.in)
Bill Discussion in Rajya Sabha on 9th April, 1977: PARLIAMENTARY DEBATES (rsdebate.nic.in)
 Article 194 for State Assembly Legislators holds an analogous position
[2[ For example, In deciding the case of Tej Kiran Jain v. N. Sanjeeva Reddy (1970) when defamatory statements were made about the Jagadguru Shankaracharya by members of the Parliament during a motion. The Supreme Court ruled that the members were immune from prosecution as "anything" said during the course of proceedings in the house is protected. This does not mean members have unrestrained free speech, as the Speaker can chose to act on those who seek to misuse it.
 Merely being allowed to speak in the legislature without public knowledge would mean the power of parliamentary privilege held a much lower value than it ought to have, especially since the privilege is given to members to ensure that issues are not impeded by constraints.
The irony of Indira repealing a private member's bill introduced by her husband was not lost when member discussed passing the 1977 Act:
Saroj Mukherjee also pointed out in 1976 that the Ordinances being promulgated together was to completely strike down the freedom of press:
Kumari Ananthan, the father of BJP Leader and current Telangana Governor Tamilisai Soundararajan observed the same on April 4, 1976 while discussing the emergency:
 Thought it did remove the Right to Property: Congress Talks Of Protecting The Constitution, Here’s What It Did To The Right To Property (swarajyamag.com)
 This was in fact what Feroze Gandhi had sought to achieve, but had to be read down to comply with powers of the Parliament. The discussions in the Parliament while enacting the Act hoped that similar provisions would be enacted by State Legislatures. The text did add some modifications to the 1977 Act as well in adoption to the Constitution.