You said that right! Absolutely. It's one thing to fix a mess in a culture that cares. It's darn near impossible to fix it if the culture around is hostile, indifferent, or any of the other 82 million other reasons organizations come up with to not care. In that situation you can end up being the pariah despite good intentions engineering and otherwise like satisfied customers.
At a big company “you” don’t lose anything. You only lose if you’re a fool trying to fix dysfunctional culture when you’re not even close to C level.