I am no longer working on Mercurial (2005)
web.archive.org
web.archive.org
Something being ironic isn’t always a bad thing. Specifically this is situational irony as the thing the creator of Bitkeeper feared (open source ripping off his product) eventually became moot when he open sourced Bitkeeper.
It's why there is the concept of the Chinese Wall - https://en.wikipedia.org/wiki/Clean_room_design
This includes public facing social media. You are now a publisher.
You can still get angry at Disney for allowing one sort of Twitter account but not others or firing people over jokes. But this is 2005, it's a bit late.
Risk it, or be secretive or get written permission. Don't be an NPC and not understand reality.
Wherever you went with this in your head, you drove past the point a while ago, I think. It is absolutely not normal for a vendor to dictate what an employee of a customer does.