This situation can be very similar to one of the ones with the relative being diagnosed with Alzheimer's above. You're concerned about how the person in question views the situation, which makes you feel anxiety. When they joke, it reveals that they have low anxiety or are in a non-threatening mood, which greatly deflates the tension for you. In that case, I'd say that the joke (without knowing much about it) greatly lowered your anxiety and thus elevated your laughter.

It may also be, of course, that there's a secondary evolutionary adaptation to laugh in scenarios where you want to demonstrate social closeness that the theory doesn't reflect. I do think that the current parameters of it can explain it though.