The problem with this statement is that it is addressing the wrong problem. No, a bicycle tire can't hydroplane but that isn't the issue here. Just because the tire can trap a layer of water between the tire and the road surface, doesn't mean that the tire can't lose traction on wet surfaces. JPprivate's tire "slipped on a very wet surface". I don't that he was traveling in a straight line when the tire slipped. He was probably turning a corner or even correcting for balance which is something that we do constantly on a bike.

I would argue that smooth tires offer acceptable traction only on dry asphalt. Once you lubricate the surface or, more properly, remove the unevenness of the surface, traction on smooth tires becomes very dicey. Think of what happen if you coat the surface with ice or paint or oil. Water isn't all that different from any of those. They serve as lubrication and reduce the irregularity of the road surface. Once you change the forces on the road by trying to change directions, that traction reduction becomes even more difficult to deal with.