"I find it hard to believe that folks who are already so good at stretching the truth to their own benefit like politicans would somehow let their personal ego and pride get in the way of them making a fake "real" apology if that would benefit them the most."
I'm sure a lot of the 'real' apologies you hear are exactly of that nature. But ego and pride don't get checked at the door when someone enters politics - far from it. Not many politicians have the discipline to be perfect PR machines at all times. Many of them seem to oscillate between politically optimized and natural states.
"It seems to me that there is some underlying calculus that all these actors have made that issuing a bogus one has a better net effect that a real one."
If we're talking about actual politicians rather than corporate spokespeople then there's always the possibility of a little dog-whistling going on. If you trot out the standard pro forma apology then most of the people are somewhat aggrieved and those who actually liked or agreed with your original statement or action can say that the apology is just PR and you don't really mean it. I can't see that happening much outside of actual politics.
"I suppose I should be thankful that if this is the case then at least we are going to be able to tell the bullshitters from the honest people, since only the honest ones will be making genuine apologies despite their potential for harm."
I don't think it's a reliable guide for the reason I stated at the top.