Conventional wisdom says so, but BFRunners are far from conventional!
You will end up with cuts and scrapes on other parts of your body during your anti-clotting therepy, and will control the bleeding with pressure until you eventually clot. In the rare event you slice your foot running barefoot, you will do the same.
Anecdotal evidence from hundreds of barefoot runners, hikers, and livers shows that we draw no more blood then the shod.
Remember......following recovery from the valve job regular cardio is key to long term health. BFRunning is more likely to allow you to continue your regular cardio activity than any other (all things considered...including when factoring in boredom such as with eliptical trainers) method.