OSI was founded by Perens and Raymond and very much represents the interests of the wider software industry. You're free to argue that at some point they have stopped in recent but Open Source has meant the same thing for going on 30 years.
The specific transition from sharing as public-domain software vs free, open, shared, and permissivly licenced software dates to ~1953 with A-2 being provided for free and requesting updates be sent back to UNIVAC. https://en.wikipedia.org/wiki/A-0_System Others might point to IBM SHARE from 1955 as being closer: https://en.wikipedia.org/wiki/SHARE_(computing)
Followed by many similar arrangements before the term open source was coined with OSI only showing up much later.
Today the majority of free software that I use seems to be Apache/BSD/MIT - and GPL for Linux - but back in the 90s everyone seemed to make up their own “free” license, and there was a lot of confusion around GPL. My recollection is that OSI was trying to create some clarity around which licenses really were “free”, and which weren’t.
I was just a passive observer, I was not involved in any way, I wasn’t a fan of some of the players, and I even thought calling it OSI was pretentious - but nevertheless they made a dent in the universe by popularising the term “open source”. OSI was far more than a rebranding because it enabled us to speak about GPL - which imposes conditions on use - and free licenses like BSD in the same breath, while excluding what we now call “source available” licenses.
So despite my misgivings, I think the OSI deserves credit. They stood up and did something meaningful, and helped move the entire software industry forward.
Because of this, I think calling it a rebranding is totally unjustified and unfair.
If you modify it and don’t give your changes back, you can be sued.
No, you are thinking of Free Software and copyleft, which predates Open Source.
Open Source was invented as an alternative to Free Software.
That's a much more diverse crowd of sponsors than I thought I'd see based on your comment.