I don't see anything that puts the cockpit crew in a bad light here; the request to "go easy on social media" was probably light-hearted and an attempt to provide a bit of much-needed levity to the situation. Plus, why the heck not make an attempt to help your employer look not-so-bad? If UA terminal staff had done their job right, this might have played out very differently.

United lost control of the narrative after the passengers left the plane. The FA not taking them seriously... that could have been no big deal after the couple had the chance to share the video with the Captain and were appropriately thanked. Things could have gone very differently from that point on. It sounds like the Captain did a great job of de-escalating the incident (without pretending nothing happened).

If I were running United, I would put that Captain in charge of any overtures to the couple. That's the only friendly face they can relate to.