but water, by definition, cannot be wet.

Yes, I've watched QI as well 😃

Of course water is wet. The US Geological Survey says "the most obvious fact about water is that it is wet, at least in the liquid state."

There are many obnoxiously pedantic people who will pick one single definition of the word "wet" in order to "prove" that water isn't wet in some sense. For example "Liquid water is not itself wet, but can make other solid materials wet. Wetness is the ability of a liquid to adhere to the surface of a solid, so when we say that something is wet, we mean that the liquid is sticking to the surface of a material."

But that cherry-picks just one meaning of the word, ignoring all the others. We can have wet weather, no solids need apply. Air can be wet. People can have a wet personality. Paint can be wet even when it is still in the tin. Places near the equator have two seasons, a wet season and a dry season.

In day-to-day language, to be wet is to be covered or soaked with water or another liquid. It's a tactile sensation that we experience when we touch a surface that is moist or damp. Water (at least liquid water) meets that definition perfectly. Is water covered with water? Hell yes. When you put your finger in a glass of water, does it feel wet? Hell yes. Water is wet.

• Dictionary.com: wet (adjective) in a liquid form or state
• The Free Dictionary: Characterized by the use or presence of water or liquid reagents
• Wiktionary: Made up of liquid or moisture, usually (but not always) water.