In fact, that was all the rage on the political Right in the US. Human embryonic stem cells, on the other hand, were condemned.
The more vocal ones caught on to the different early on because it was important to them.
A lot of others sort of glossed over the difference because, well, effacing the difference was important to them. Or they couldn't wrap their minds around the difference.
These are almost certainly adult stem cell transplants. Probably very similar to the bone-marrow transplant that they modelled the therapy on. No fetuses or anything-blasts were involved in the process.