Within their rights to enforce their policies, yes. Wasting their time even attempting to do so? Also yes. (I think this was DCP2016's original point.)

Optics win on this one.

Not sure how viable it is, but there's currently a petition in front of the Department of Transportation that calls for the DOT to “reject airlines’ improper attempts to prohibit recordings by passengers of events on-board common carriage aircraft and their interactions with staff."