Well, unless we find some video footage we won't get a solution, but...:D
I listened to it a couple of times now and I still think that they share a mic.
I see your point with the harmonies, Walleris, but the chorus in that song doesn't have harmonies.
Regarding the loudness, Dominik - Richie is much louder than Jon, that's why you think he's singing lead :D You can still hear Jon singing the chorus as well, just not as loud because of Richie's voice.
Just watch and listen to other performances where they shared the mic (e.g. the first bridge from I'd Die For You from Montreal 1995, beginning at 01:00
), it's the same...let's call it "vocal pattern" or loudness level between their voices. Richie's dominant voice with Jon's quite lower one in the background.
And besides those points, it wouldn't make any sense for Richie to sing lead on that one. Why would he?
1) Jon wants him to shine? Than he probably would have made a short "announcement" like "come on, Richiiieee" or something like that or some wild gestures that would have made the audience going wild - but none of that can be heard. And in that case Jon wouldn't sing the chorus, too.
2) Jon has a vocal problem and thus wants Richie to help him out? In that case Jon wouldn't sing it together with him either.
Additional to those 2 points, you can hear Jon start singing the chorus before Richie kicks in which doesn't make any sense, too, if Richie is supposed to sing lead.
3) Jon has nothing to do with it but Richie decided to sing lead from his sidekick-position? Come on, even in 2013 Richie wouldn't have dared to do so :D