I'm pretty sure this is only true in certain conditions. I've seen p.o. in autumn when it's "ripe," for lack of a better term, and the oil's almost oozing out of it.
I'd imagine that's a far different beast than a young shoot in springtime. Also, I believe different strains of p.o. exist (based on what it looks like in NW Indiana compared to its appearance in several other areas to which I've traveled).
Anecdotal evidence only. Personal experience.
Edit: You are correct that if it's cut or damaged in some manner that it's easier to get the oils onto you. I'm just saying that just because a leaf or plant is not cut or visibly damaged, it can still transfer the oils.