Like do people actually have bins that are open and under the actual sink?

Yes, tons. We have to keep all our trash in cupboards or locked trash bins because 5 cats and 2 dogs, one of which is 50 pounds, will knock them over constantly to get at our delicious human food lol. I've also just seen it in a lot of other places from other people. If you don't have a lot of room, or want it hidden, the kitchen sink cupboard is a great place to store garbage.

Ironically, I've seen tons under the sink but never a door mounted one. Regional differences/tastes probably account for a lot of it.

But either way, you have to open said door to throw the garbage away whether it's on the door or underneath the sink and it would be incredibly difficult to do so without seeing there's no can to throw the trash into.