Is it that simple? It certainly does not fit my experience. I type code for a living and have for 30 years so I'm clearly well rehearsed but I can't type well when being looked at.
This is psychology, there are always exceptions. Personally I don't have problems with the act of typing when being looked at, but I do have a tendency to get nervous to the point I'm having trouble speaking. Only happens with crowds I'm not familiar with though. But I know enough of sociolog/psychology to realize that doesn't mean any of the claims made here are false for the general public, or even for me in certain situations. I do have the impressions I'm sometimes better in sports when people are watching and/or cheering.
Perhaps that is not a performance, in the same sense as other stuff. e.g. do you get a bit of adrenaline kick in, are you motivated to impress them with your keyboard skills, etc?