What I was trying to say was that money is only true money when it is defined by political authority as legal tender which must be accepted. And only official money meets that requirement.
Of course, if the private money is of more value because of the market than the official money one would have to be a fool not to take it but it would be within his rights to refuse it.
I will check out the book you reference it does sound fascinating.
If you're interested, Selgin also gave a talk about his book at the Mises Institute a couple of years ago.