This is the correct verb. desternilló and not Destornillarse which means having a screw loose. To laugh uncontrollably or “break one’s cartilage” (from ternilla, meaning cartilage) from laughing so hard.
OP is saying the sentence is correct, which it is. The expression is ‘desternillarse de risa’.
I guess what prompts the comment is that it’s common (among natives) to say destornillarse here, simply because tornillo is a common word, ternilla they’ve never heard, and the switch kind of makes sense semantically.
It’s 100% correct. But as Daniel said, it’s easily confused with another verb. I commented to help myself and others who came upon the sentence because the translation engines don’t interoperate it accuratel.