Indeed it is public but that means it's my chain as much as it is your chain. Therefore, provided what I do with it is within the accepted rules (which it is), my right to use it how I like is no less valid than yours.
For avoidance of doubt, I want to make clear that I'm not inscribing data habitually like some maniac. In fact I very seldom do it and when I have, it has been tiny because that's part of the challenge.