Leaving aside all the hundreds of ways they could easily resolve the situation here *without* the webcam exposing their identities...
... to say nothing of thinking simple bondage will keep Dick down. I mean, seriously...
... there is no way these guys would wear loose-fitting boxers under those tight and form-fitting super-hero outfits. No way. Boxer briefs, or some kind of athletic support (and Bruce would've been an idiot to never use an armoured cup, or whatever) -- but simple boxer shorts? No way.
Damn it, if Dick's gonna be tied up in his underwear, he'd better be wearing skimpy briefs or a thong or something. I can forgive the lack of common sense, but the wasted opportunity for pure fan-service -- not cool DC. Not cool.