As someone that tends to travel armed only with my wit:

Doesn't it just mean that they want you to have the keys with you, for the exact purpose that you describe? That would seem to me to be the common-sense interpretation.

Maybe they had a few situations where they asked for the keys to inspect, and the owner of the case couldn't provide them, which seems to me to be a neat run-around of the inspection process (in which TSA wants to be able to open everything).

Requiring you to have the keys with you solves that scenario unambiguously.