There is a youtube video of Pinnocchio titled "world's smallest dog" It says he only lived a couple of years

I heard that the tiny ones aren't that healthy and don't live a long life.

Who'd want a dog that lived in a bird cage anyway?
I doubt the girl's dog on FB will stay tiny, tiny. Most grow a little bigger then you expect especially after spay and neutering. I consider 3-4 lbs a tiny tiny.