I'd never heard of this before, but from the bit of googling I've done since you asked the question, there's really no agreement among yogi.

However, the issue as it's framed on many sites online has to do with the flow of energy, not flow of menstrual blood per se. Since yoga as a discipline deals entirely with energy flow, I'd be inclined to err on the side of caution. Is it really a big deal to skip inversions for one week each month (and instead, favor some of the poses that are recommended during menstruation)?