Can spent transactions that get pruned lead to false payment claims?
Sure, but so what? I can make all kinds of false claims that nobody can disprove.

We only care about two things:

1) Can someone who actually has funds prove that they have those funds?

2) Can we ensure that somebody who does not have funds cannot prove that they have funds?

So long as we meet these two criteria, there is no problem. It's perfectly fine if people can make claims to have funds that we cannot disprove, so long as they cannot prove them.