Native speaker here, and vertical crawling is definitely odd for a human. If the motion is more vertical, up or down, I'd tell someone learning English to default to "climb."
That said, "crawl" is not necessarily wrong for an insect. I think the distinction is that "crawling" implies relatively little effort, so for an insect (or a spider or a gecko or something) it's basically no different for them if they're crawling down the wall as opposed to along the floor or ceiling. Anything that has to go to extra effort to fight gravity you should use "climb" for. (Squirrels are maybe the border case? I'd think it's a little weird to say a squirrel crawls down a tree, though not necessarily wrong, but a monkey would definitely climb down, not crawl.)
I'm not a native speaker, but it still strikes me as odd. If I google for "vertical crawling", I see pictures of insects, some impressive offroad trucks, toddlers (definitely moving on a horizontal surface), and... Spiderman. Okay, granted. He's pretty much the only human I can see crawling down a wall. :)
But I have to admit that moving vertically isn't the only possible interpretation here. Just the first one that comes to mind. You could crawl down a slope just as well.