They probably don’t, but they have families to feed, so it’s better to follow the guidelines and lie to a bunch of anonymous people on the internet rather than have your wife and kids beating you up after losing your job due to “not being evil enough”
I think they mean EA Anti-Cheat, not Easy Anti-Cheat. The former, which is used in 2042, does not run under linux (and probably never will).
BFV runs out-of-the-box on linux systems and has a “Gold” rating on ProtonDB. If EA really goes on with this, BFV will become unplayable, just like 2042.