Guys, it's really not worth even arguing. Both healing types CAN exist in the same world, or can be excluded with the selection of classes fairly easily. Not only that, but the ways in which both sides of the fence, divine and non-magical healing, are represented in play is truly on a game-by-game basis. It can be as realitic as momentary field dressings, dramatic, uncanny, or silly as you like. There's nothing to argue here!
You're both allowed to play how you like. And if one or the other party can't conceive how it's more or less believable to the other, that's okay too. It won't affect your game. Stop dictating what is believable to the other person, and what stretches each others' disbelief.