As long as we aren't talking about infants here, it's been a loooong time since I dealt with that. But in the winter time depending on how active they are I'd say no, they don't need to bathe everyday. Once they get up in years to teenage then yes. So it depends on the kid I guess.
My kids are 9 and 12 and come summer they will be bathing about everyday depending on swimming too because they try to tell ya that swimming counts as a shower

I think they are allergic to soap or something
So in a nutshell Ben, I believe your wifes' statement could be considered correct.