Can spent transactions that get pruned lead to false payment claims?

Question

The bitcoin white paper says that spent transactions get pruned after being buried behind enough blocks:

7. Reclaiming Disk Space
   Once the latest transaction in a coin is buried under enough blocks, the spent transactions before it can be discarded to save disk space.

At some future point after a transaction gets pruned, couldn't the original recipient of that transaction then claim that she did not receive the correct amount of payment without worrying about anyone being able to disprove her because the transaction no longer exists in the blockchain?

Answer 1

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.