Well, I'm not on your friends' list, but I just scrolled passed this and I'm German so I figured, why not.

>So. My question is this. Is what people are saying a legitimate grievance? Or is it just people's personal preference? Because if I see one more person say that, and I quote, "no one would use language like that", I may just scream.

I seriously don't understand why people would say that those terms are outdated. "Schatz" is probably THE most frequently used term of endearment amongst couples.
"Liebling" is, I guess, slightly less frequently used and possibly the teensy-tiniest bit old-fashioned, but that depends very heavily on your personal point of view.
To me, these are perfectly fine, and now that I think about it, I "Liebling" is probably the most used translation of "darling". So, it's all good.

And now I'm trying to think of other ways to call someone "darling" in German, but I'm somewhat at a loss. There are endless numbers of (mostly rather ridiculous) petnames, but I'd always go for "Liebling".
There are variants, like "Liebster", but that one I would definitely call old-fashioned.

I hope that was of some use to you.