I think getting the head through and being able to get the rest of the body through is true.
I think rats are supposed to have really bendy skeletons, and they're supposed to be able to actually compress their bodies by lengthening themselves and squeezing through that way. I guess the organs actually move around when this happens. I'm not sure, but I was looking at an image of a rat skeleton and it looks like the bones that make up the rib cage are each two jointed pieces, allowing them to actually compress the rib cage.
That's roof rats though. Certain fancy rats are pretty chubby since they're domesticated, and mightn't be able to do that the same way roof rats do.