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Twice, just like you in the vid, it was like being in a "downed" state in Firestorm (except I was in regular MP). I could shoot, use my gadgets. I don't think my bullets were doing any damage but I got a grenade rifle kill (lol) and an AP mines kill after I put 2 down next to my body. Switching squads and attempting to redeploy did nothing. I was able to be revived though, so I guess to my team it showed me with the "revive" icon next to me.
I also saw it happen to an enemy, I could tell because I could hear them shooting at me, but all I could see was a dead body. For the lulz I teabagged them a bit and then left an ammo crate next to them so they could continue on.