Well, of course the entire argument about getting used to the coat's warmth and feeling colder once you get outside is complete nonsense. I'll concede there is a tiny grain of truth in the "get used to it" hypothesis. To me, 40 degrees certainly feels cooler in August than it does in January, in part because in January I'm "used to" the cooler weather. But that's also because I've had several months to acclimate, whether to cool or warm weather. You're not going to make that swing in a few minutes.
So stand up for your right to put on a coat any damn time you want. Don't let those feisty San Fran people intimidate you.