I've never had a pet with a higher level than 5 go down to level 1, but it's been a while since I've labbed a pet with a low level and that might've changed. The cutoff (if there is one) just means that your level can only go down by increments of 1-3(ish), not all the way down to level 1. You can still go below level 20 or whatever the supposed cutoff is, though, so be careful.
(There is a school of thought that says that the 'down to level 1' result is just there so that a level 2 pet doesn't lose 3 levels--it's just a stand-in for losing more levels than you have. Not sure if that's true.)