That's what baffles me a lot. I love Def Leppard and I do think they sound amazing. They manage to have a sound engineer which can really make the setting work for them. Burry the difficult parts into loud guitars etc.

I just can't work out if they use backing tracks for backing vocals or not. Their vocals sounds really perfect. And they like to mention it in every interview that it really is just them live. I'd understand if they used a backing track. But I don't think they'd put so much stress on not using it when they were using it. I'd expect them to shut up about it like Bon Jovi do.
On the other hand, there obviously are many samples programmed or Rick's drumkit. There's a special setting for almost every song. They don't talk about THAT when it's obvious you need some tricks when your drummer has only one arm and your music relies on many sounds and drum patterns.