Bad argument or not, I still say it's a bad idea to constantly shovel hair covered rodents (exclusively) into a garter. That's just tempting fate. I take it a step further, and avoid giving them hair at all. Besides, most garters I've had will instantly drop a hair covered mouse but will gladly take naked ones.

A partial blockage, injury, etc. alone isn't the problem, but introduce wads of undigested hair and you got yourself an issue.