If a premise is demonstrably untrue, does it automatically beg the question?

First, I'll admit to using the phrase "begs the question" incorrectly in the past. Having just finished lesson #9, I wonder if it wouldn't always be appropriate to follow up a Begs the Question fallacy with, "That's not true because," even if only doing so in my head, so as to identify the fallacy that just occurred and plot a response.

But for something to beg the question, it doesn't have to be false; it just has to be unproven. For example, if I were to say, "Why do you think police officer X (no relation to professor X) murdered that innocent man?" There are three significant assumptions here: 1) that police offer X was the one who committed the murder, 2) that it was "murder," and 3) that the man was innocent. It very well may be the case that this question contains factually incorrect information, making the entire question fallacious. However, it is also possible that the assumptions are all true. A better response would be "That has not been established yet."

Oops wrong place....To throw fuel onto to merit of logic viewpoint. Valid is synonymous with sound. In logic, valid is not synonymous with sound. Now that's logical, jk. Lol