Don't we pretty much understand stars though? Big ball of gas, hydrogen fusion, etc. Are there any unaccounted energy outflows that would leave room for something like this?

The main reason we look at black holes so hard is because quantum mechanics can't describe gravity (yet) and general relativity just shrugs and says "I don't do inside event horizons, buddy, but why do you care? You can't even experiment inside one". So it's one of those head-scratchers where the math isn't really helping us figure out _what_ is going on, and the darn things are really hard to observe.