Do you think we can't have physical contact with anything?

So I've heard.

we can't touch anything, we can only get really really close to it.

sounds like a strip club to me...

a philosophical conundrum.
"How close must you get to something before you touch it?"

Yes, it is a conundrum indeed, an interesting one at that.
I am guessing that if the two surfaces where the atoms chemically bond to one another, then in a sense it could be labeled as touching. It makes sense to say if two objects are touching, then there must be a self-connected object which overlaps both the objects which in this case are the electrons that are shared; in other circumstances, the electrons will repulse and just avoid one another, thus could be labeled "non-touching."