“Guaranteed: It didn’t take “30 minutes” for the crew to figure out they had a flap problem after takeoff!”
For sure. But as long as the flaps are not asymetrically jammed, it’s not a critical emergency. So they have plenty of time to make sure to comply with the specific emergency procedure for this special case. Notify ATC, check hydraulic pressure, switch hydraulic circuits to alternate hydraulic pump, dump fuel (might take a lot of time depending on how much fuel needs to get dumped), rebalance the plane while dumping fuel by pumping fuel from one fuel tank to another, ...
Flaps on big jets have mechanical links that freeze their position if a significant asymmetry is sensed during movement (stopping before the asymmetry is enough to notice). But then the flaps are frozen in position which explains their return to the same airport. If the flaps are frozen in a near- retracted position then the approach speeds will be much higher than normal (even after dumping fuel), leading to other problems such as landing distances too long for available runways, high angle-of-attack approaches at high air speeds, hot brakes, and possibly even blown tires.
The nature and seriousness of the problem was likely unknown to the passengers.
Maybe the passengers who stayed on the airplane had been drinking and were afraid their alcohol consumption would be noticed by the Saudi authorities if the got off the airplane!