It looks like the percentage of Americans vaccinated may not be nearly as high as the official numbers. Multiple states vaccinated more elderly than they had so the number vaccinated is pretty much guaranteed to be higher than the official numbers. One state basically vaccinated 150% of their population.
Discussion
If that link doesn't work, check out this one: https://kirschsubstack.com/p/in-california-weve-vaccinated-more
This was definitely the case in the UK, can’t remember the exact figure but far more not injected that was first reported