Having previously worked in ground handling, "operational reasons" is cited for a number of reasons. Yes, sometimes it's due to a lack of crew (i.e. we messed up and don't want to admit it) but sometimes it's due to a late inbound aircraft, or rather than telling everyone about a technical fault which could potentially cause nervousness I always used to say operational reasons whilst the engineers were investigating. Once the issue was confirmed I'd then refer to it as a technical fault because we'd often have a bit more information to back it up.
Similarly when an aircraft is ready to depart, the dispatcher and flight deck will agree reasons for the delay and assign a delay code. Both parties must agree on the delay code, so if the captain were to say one reason to the passengers, the official reason, and therefore the reason that would declared in the event of an EU261 claim, would be the truth.