I'm a redhead too, and definitely giving this the side-eye. It's an idiotic myth, if you ask me, it would make me wonder what other weirdo things the midwife believes. Having red hair does not mean that your clotting factors are somehow screwed up. It also does not mean that your uterus is floppy or won't stay contracted after delivering the placenta (which is why people generally hemorrhage). Having red hair usually only means that you're pale, so bruises show a bit more than they do on other people, which (apparently) leads some people to conclude that you're part hemophiliac, or something.
FWIW, I had my first LO at a birthing center with no IV fluids, no heplock either, and no hemorrhaging. I also work at a hospital maternity center and none of the L&D nurses I know believe in the myth, either.