I think you always gotta be leery of anything that's got fresh paint on it, primed or otherwise. Recent paint can hide a lot of stuff.
Did you look hard at the areas where these trucks typically rust i.e. the front fenders right behind the wheels, the rockers, the cab corners, the lower door skins, around the top of cab? Was bad metal replaced with patch panels or were rust holes filled with Bondo? If the floor's all rusted out, you know plenty of other stuff was or is rusted out.
Hard to say without seeing it but, based on what you're saying, I might go $2000 IF, there's new metal on the body and not a bunch of filler.
There's a lot of 60's trucks out there!
