We need different words for apology in the sense of "I'm sorry; I won't do it again," and apology in the sense of "I'm sorry that this lowers your utility, but not sorry enough to actually change the behavior in question; maybe we could negotiate some other behavior change that might partially make up for it." Both can be sincere, but they mean different things.
I this Zack, I think I'll borrow it (use it?).
The former is likely an expression of remorse; the latter an expression of regret, i.e. "I regret that your dog attacked me and I had to shoot it."