Ummm...no, it doesn't. Remember what I do for a living?
Those claims are complete BS. Your blood cells carry all the oxygen that they are designed to carry and nothing will change that. You can add more blood cells with EPO or naturally by living at high altitude, but you cannot increase the oxygen carrying capacity of them...especially not with beet juice.
Yeah, we pharmaceutical scientists have completely missed that natural wonder called 'beet juice' that we could turn into a billion dollar drug...ummm...no.