"Saracasm aside I would not have accepted their "authority" in this regard and have requested clearance to IAD."
"Authority" has multiple meanings.
Did DC TRACON have "authority" to require the planes to land at DCA? - No. That authority always resides in the cockpit (via an MAYDAY if all else fails - viz. AA captain at JFK not too long ago).
Did DC TRACON have "authority" to declare DCA temporarily uncontrolled, and thus available to the planes IF they wanted to use uncontrolled airport procedures, even in the absence of a tower clearance to land? Apparently TRACON thought so, and apparently the pilots thought that was preferable to a diversion to IAD or elsewhere. (Whether the TRACON actually had such authority will likely come out in the wash - but I don't see that it's the crews' headache to sort out the FAA's internal legalisms; they aren't paid for that.)
You'd have done something different - and I would not fault you for choosing a diversion. These guys chose the other option - and I don't fault them, either.
In some aviation situations, there are no right answers - in this case, I'd say there were two right answers, neither absolutely perfect.