How long does it take garlic to germinate in the fridge?
Germination of garlic is a gradual, slow process, and how long it takes depends a lot on how close to sprouting the garlic was when you originally bought it. Seems to me it would have to sprout faster at room temp, than refrigerated, anyway.

I routinely keep garlic in the fridge (shame on me!), and sometimes the garlic will keep in the fridge for at least a month without sprouting (That's about how fast I use it, so I don't have data past a month). On the other hand, I have seen nubby little green/purplish sprouts (abt. 3mm long?) on garlic which I had just purchased; cut them off; garlic was fine - just like your experience. 

I guess the reason you want to keep the garlic in the fridge during your stay at your friend's house is to avoid unnecessary rancourous arguments - yes? So here's the thing: your friend may be wrong, but for the layman, it's not a huge deal to keep the garlic in or out of refrigerator, as he likes.