Any truth to de la Mesa origin story?

I tried to find any mention of it on the web. Seems like a lot of Spanish surnames are location based. Soto = grove, forest, or swamp. Castillo = castle. And the only explanation I found for (de la) Mesa is for one living at or near a plateau.

So was the torture thing made up because it is good story? or could it be some Mesas got their name from plateau residing while a few got it from torture presiding?