I don't think the fighter shares any blame. It's not his job to tell the ref the fighter is tapping. It's the ref's job to see it. I actually think it's a bad idea for fighters to tell refs their opponent just tapped.
They shouldn't be influencing reffing of the fights that way. I also get annoyed when I see fighters look or yell at the ref while they've got a sub locked in or are landing GnP, trying to get the ref to stop the fight. Focus on finishing your opponent and let the ref handle the stoppages.
Couldnt put it better.