By "in the corner, so it's out of the way" do you mean inside of the enclosure, but not placed in a distracting (visually or physically) location? If so, then despite it being able to regulate the temperature as you described (without direct contact), I would contend that it's not placed in a position to perform optimally.

My reasoning is that a thermostat probe placed on the inside floor of an enclosure is subject to "the elements". "The elements" can be any number of factors that would cause a probe to not report reliable temperatures: contact with liquid from spilled water or urine, being moved from it's original position by an active snake, a snake getting comfortable between the probe and the floor of the enclosure, and any number of other events that happen pretty regularly on the floor of an enclosure. The best way to protect against "the elements" is to place the thermostat probe out of the way on the outside of the enclosure where it is able to report reliable temperatures pretty much regardless of what's happening on the inside.

You are spot on that the probe does not have to be in direct contact with the UTH in order to be successful, but it sure makes a thermostat a heck of a lot more reliable/responsive/accurate/safe if it is.
I was only referring to a probe being used inside the enclosure, and not with a UTH. I agree with you that there can be some unwanted factors like the snake laying on the probe, or liquid contacting the probe that will change what the thermostat is reading; and you're right, the probe is better placed off the ground to eliminate those problems.