Yes vinegar will only kill the vegetation. But, imho, poison ivy vines are easier to handle without the leaves on them. Urishoil is a nasty beast and the less of it I have to work about the better. You can still get it from the vine, from ALL parts of the plant actually. But it's easier to handle carefully without leaves.
I'm a bit then in that approach actually, as it makes ID All but impossible. But the alternative is to have urishoil ALL OVER THE PLACE. there is just no amount of protection I can take that avoids contact. I'm just trying to minimize it. In the picture below you can see what I'm dealing with. You probably can't tell from that photo, but there is possible to ivy all through this. Mostly small vines here. The big stuff is in the background beyond the bed, but that will have to go too.