Heck, Charles Atlas constantly trained, its the trope, but if you compare that to a Shaolin Monk, is there really any light between the two? Charles Xavier did it all by standing around and exercising his mind, purely, so we can that these things cannot totally be lumped together, but they're still all merging at some point.
In a sense maybe 'power source' wasn't that great an idea. I mean, it works in some fashion to generally categorize, but its not a 'clean' facet. Divine and Arcane (and Elemental, really Shadow too) don't cleanly separate either. I think that its best to think about it in 4e as literally SOURCE in a very simple way and just decree that the universe works this way. You can get pretty much the same effect from Psionic/Qi as you can from Martial, but they are still manifestations of fundamentally different kinds of power.
That kind of says to me that while multi-sourced classes aren't ridiculous, they can exist according to the paradigm, they may not really be the best thematics. It might be better to just say "well, I achieved this melee weapon fighting effect using divine power, that's just how my class works!"