I recently watched a coworker lose a job by embodying this very logic. I think the problem comes from the conflict between denying/rejecting victimhood, on the one hand, and realizing that one must get the fuck out of a very, very bad situation immediately, by any means on the other. From what I could tell it quickly becomes an inescapable cycle between "it's always my fault and I'll fix it"-- which implies leaving--…
Asking for help is a perfectly encouraged way of fixing a problem. That's just a modality. You're still taking ownership of the situation and making steps to remedy.
I'd go so far as saying that asking for help is often the quickest and fastest way of fixing an issue. People can't help unless they a) know you need help and b) know what kind of help. Just sitting there fuming in your victimhood won't inspire people to rush over and help.