Millie is spayed since before 6 mos and she marks all the time. Not in the indoors, but when we go for walks she sniffs other dogs and marks on top of their smells. She also pees every five seconds on our walks.
Female and male dogs mark. I don't think it's as rare as the vet thinks and I am not convinced it has anything to do with their alpha status either. (but I'm not a professional, either

)