The trans person is "dictating other people’s words" in one, very limited context: when referring directly to that person.

Given that the only obvious reason to actively refuse to use their preferred pronouns amounts to a pretty deep attack on the legitimacy of their identity, you can see why it would not feel like a trivial thing.

You might be similarly intent on insisting that people call you <actual name> rather than <offensive nickname>; that's just as real an example of "dictating other people's words".