You are right BUT as i mentioned in previous lesson, we don't have to strictly follow the theoretical basics and than we can get totally kick-ass sounding chords. In this case - the chord i play with E sound MUCH better than if we played it with G.
We can say it's a Cadd2 (C added 2) but again we only add it on B string. That's why i always say:
"Don't go for 100% theory, scales, diagrams and all the theoretical stuff. It is useful BUT it also prevents the imagination from working because you are concentrated on mathematics rather then sounding."
All the lessons i have written for GMC have some rule exceptions. I said Csus2 because it's the closest to Csus2 but there can always be some notes outside the chord but it doesn't mean it's mistake.
Music is not about rules - it's about how it sounds!  I hope this answer will be good for you!
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