I don't like to see people being hurt.
Maybe I don't like to see people in general, but that's not what that sentence means.
Similarly, yours says that you don't like those sorts of rumors being circulated at that time. Presumably, you don't like any sort of rumors, but that's not what your sentence means. One could imagine that you perhaps condone them as a rule -- but not "at a time of deeply personal grief".
Also, "sort of" qualifies "rumors", not their circulation .