The entire match was choppy and occasionally it would stop and the loading symbol would pop-up, so I doubt things were going well on his side, though I know what you mean.I don't think all lag is universal. I've played with friends who said they were getting stuttery lag while I only saw the normal input lag.
The person taunting during what you see as a laggy match may have no idea.
In fact I may have ran into this exact situation today. I fought a and there was so much input lag on my side yet he seemed to move just find. I get hit like once or twice in the first 15 seconds (had about 12%) and didn't feel like fighting through a laggy match, so I intentionally kill myself by riding my bike off the stage. Of course being For Glory the Roy spams his taunts like me purposefully killing myself was all his work, and teabags when I take my second stock. If I had to guess his connection was smooth while only I had input lag.
I seriously wonder what was going in that Roy's head while I killed myself: "WOW THAT GUY IS AN IDIOT IM SUCH A GOD AT FOR GLORY!"