'The Crying Game' and 'Secrets and Lies' weren't Hollywood films. Neither was Boys Don't Cry really...not a Studio film certainly. But sometimes you can't give away what a film is about in previews without spoilers. I obviously question the designation of Million Dollar Baby as propaganda for euthenasia. It was rather ambiguous on that score. And 'Far From Heaven' was more about 1950s movies then anything else...just sytematically inverting their cliches...all it really did of course was create new ones.
Very few production companies nowadays have no ties to Hollywood.