This question comes from a curious debate I'm in the middle of. Thankfully it's a completely wound-free debate (physically speaking). But I'm not certain if a rubber bullet wound is 'real' gunshot wound legally speaking. Have there even been court cases or public policy referencing it?
There's no statute that I'm aware of that would require it. First, it's a bit of a slippery slope once you start reporting things that hit you and hurt. Who is to say what actually caused the impact? As far as I know, your GF hits you with a pointy end of a broom, it's gonna look a lot like a rubber bullet hit.
A bullet hole leaves very specific wound and it is testable. Often times there's even a little metallic piece that confirms the shot.