Can rabies spread through visibly unbroken skin?

I was recently denied the rabies vaccine on grounds that my wound wasn't visible. I've been looking at several sources on how the virus spreads and they all mention that the skin has to be broken, but does it mean broken to the naked eye?

A minor scratch where the skin appears unbroken and there was no bleeding could still have microscopic breaks of the skin, therefore it seems risky to rely on the naked eye.