I think you are right and that it very much depends on the school. At my D’s HS, the AP track was much more rigorous than the DE track. Weighed the same in terms of GPA calculations, but not considered the same when the GC designated the amount of course rigor to colleges.
You’ve gotten good advice - I would talk to the GC and see what kind of information they send to colleges about the DE program.
I will also add that at my D’s OOS public flagship, the AP courses were easily transferrable but the DE classes were highly scrutinized. She knew prior to committing what would count for APs but didn’t know until a week before she registered for classes if her DE courses would transfer.