I could be wrong (and if I am, I am positive someone will correct me) but - I don't think you can control someone else's decision to connect to a profile in your tree (thus getting alerts when you do something to that profile). I am pretty sure that you can only control with which trees you yourself wish to be connected (that is, the ones that will generate alerts to you).

What you are describing is not a problem generated by someone connecting to your tree (where they would get the correct information - which is what you want), but someone connecting to the other (incorrect) tree, copying from it, and spreading the errors in it - which you certainly would not be able to prevent.