Re: "ban people based on their legit OS and legit game"
It's a legal copy, purchased using real money lawfully earned.
What it isn't is running on a supported operating system. EA are responding to their software informing them "Unable to validate that this software is not being run on a copy of Windows with no known cheats active", and it's correct, it's not.
Had EA banned them on that basis, they wouldn't have a leg to stand on. Because EA banned for "for cheating" there's a lot of fuss and silliness on the internet.
I do think a refund would be appropriate, and also an apology for claiming that they were cheating. I don't think supporting Linux is necessary, but I also don't think the people that have been banned were doing anything wrong either.