Why checking if tuple belongs to join of two tables is NP-complete?
If the claim is:


  for instance, given a join query $Q$ and a relational database $D$, checking if $Q(D)$ returns a tuple is NP-complete as well


the NP-completness is about the decision if that join operation returns an empty set or not (for instance because the join condition is not satisfied by any pair of tuples).

So, if this hypothesis is true, the claim is not, as you are asserting, about the fact that a certain tuple belongs to the result or not (for instance this could be checked by verifying that the tuple satisfies the join condition).