Well, there are many Scottish-based companies trading here in England too - I'd be very sorry to lose M&Co., and Farm Foods, and so on. I hope it's scaremongering.
I doubt there will be much direct effect on the branches that's what you mean? Not immediately anyway. I suspect it's likely the likes of HBoS and RBS may relocate their Head Offices away from Edinburgh though. They may well rebrand at least outside Scotland in order to downplay their Scottishness also. Can't see any way in which a Yes vote would be good news for the Scottish based banks though.