For US domestic purposes, delay vs. cancellation is a distinction without a meaning. So, the agent's confusion was entirely appropriate as front-line agents don't provide legal interpretations and it is irrelevant.

All that matters is whether the delay was within DL's control (typically a mechanical) and whether the length of the delay necessitated a hotel or food (which it did).

So, OP's post is missing the one critical detail, e.g., why was the flight delayed? The rest is all a red herring.