Arob, I suggest you look at this link, courtesy of Tadao. It might help your understanding of the problem.
To your point, I believe one of the problems with cord blood is that only about 1 in 10000 red blood cells in cord blood are, in fact, stem cells. The trick is to separate this 0.01% from the whole. Which is currently not possible.
Again, I'm not a "MEDICAL" doctor, so I reserve the right to be completely full of shit.