Only saying that because couple years age son was having same problem ,climbs up on the roof looks down the chimney ,out jumps a squirrel almost knock him off the roof .
I'm sure it happens. LOL. But this is a 7x11 tile inside. I don't even think one squirrel would stop it enough unless he got all the way down at the stove pipe. (and he likely would have still been there when I opened it)