https://www.resetera.com/threads/gameblog-fr-kojima-secretly-used-a-part-of-mgsvs-budget-to-develop-and-release-p-t-without-konami-knowing-this-was-a-reason-why-he-was-fired.234025/
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Obviously nothing is confirmed so take with a grain of salt. A quick TL;DR if you don't want to read the whole thing.
P.T was developed in secret by a small team and a very limited number of people knew it was going to be released (seems like battleship but ok)
Important people at Konami who needed to know it existed did not know and first found out when it was announced at Gamescom 2014 alongside the public. This is apparantly the straw that broke the camel's back when it came to Kojima's relationship with Konami
Kojima (who was Vice President of Konami at the time) worked with Sony to create a shell company in order to publish P.T on PSN while most employees at Konami knew nothing about this
As a result, Konami PR found themselves having to answer questions from eager customers about a Silent Hills once the news came out that P.T was a playable teaser for a new SH game
One of the main reasons Kojima was fired from Konami was because he used part of MGSV's budget to develop P.T
Kojima didn't really have to report to people and his freedom within Konami at the time was a point of major tension between the two
The heat between Kojima and Konami is gone now and communication between them has resumed, an avenue of collaboration between KojiPro and Konami is possible
The full article is here: http://www.gameblog.fr/news/91090-revelations-sur-les-plans-de-kojima-pour-le-dlc-de-metal-gea