I was fighting Mr. Bigglesworth not too long ago,and it was probably the closest match I had ever played. Unfortunately, I was bested, and my character plummeted, unconsious, to the ground. Wierd thing is, his did the exact same thing not one second later! They just laid there for about 10 seconds, not moving, as I and Mr. Biggles wondered if the game would freeze. Thankfully, it didn't, and the next match came up soon enough. We finished the game successfully.
Has this ever happened to anyone else?

Yes and with only one other person. Guess who... RagingDemon3k.