Desktop A/C unit. This can't possibly work! Prove me wrong?

Prove me wrong, please?

edit: thanks for all the great comments, this is really helpful. My main take-away is that it does work, but requires dry air. In humid conditions it doesn't really do anything.

Spouse bought this thing that claims to cool the air by blowing across some moist pads. It's about as large as a toaster, and it has a small water tank on the side. The water drips onto the bottom of the device, where it is soaked up by a sort of filter. A fan blows air through the filter.

1. Spouse insists that the AIR gets cooled by evaporation.
2. I say the FILTER gets cooled by evaporation.
3. Spouse says the cooled filter then cools the air, so it works.
4. I say the evaporation pulls heat (and water) from the filter, so the output is actually air that is both warmer and wetter than the input air. That's not A/C, that's a sauna. (Let's ignore the microscopic amount of heat generated by the cheap Chinese fan.)

By my reckoning, the only way to cool a ROOM is to transport the heat outside. This does not do that.

We can cool OURSELVES by letting a regular fan blow on us = WE are the moist filter, and the evaporation of our sweat cools us. One could argue that the slightly more humid air from this device has a better heat transfer capacity than drier air, but still, it is easier to sweat away heat in dry air than in humid air.

Am I crazy? I welcome your judgment!