It would be hard for a spider of medically significant size to suck down their exoskeleton like that.
I do believe there also is a song about them. It goes something like this: Anywhere you go, you always take your spider, your spider with you... ;)
Not knowing what spiders are "jumping spiders", I felt like those attributes are what makes many people freak out about spiders in the first place. Looked at some images and yeah, those look way worse than the spiders I have in my house, probably because of those freaky eyes and the thing having fur.
They're not insectlike, but in some weird uncanny valley between insect and mammal.
And they can JUMP onto you.
Nope nope nope.
They will play 'catch the laser dot' with you like a cat does or even do little mating dances when you prop a mirror in front of them.
YouTube has many videos of such activities
Have a bit of fun with them next time you see one and your next encounter will not be so unpleasant!
-ex arachnaphobist
[1]: https://en.wikipedia.org/wiki/What_Is_It_Like_to_Be_a_Bat%3F