This would count as a reason not to believe him, because students already know enough about science to know that’s just the wrong kind of argument to make.
Of course, the professor needs to make good arguments! But students initially don’t know all that well what good arguments look like, so they have to be guided to go through the motions, like in any other craft. Science is a craft, and we need master craftsmen to guide us so we can devellop their habits. As we accrue those habits, we need teachers less and less. My physics students believe me more than I would like, to be honest…
And also, who are we kidding? None of us have time to re-prove everything. A lot of things - maybe most things - we take on faith that our fellow scientists have done their job. Paradoxically, I think this is true even for the researcher who has to question and disbelieve “everything”, fully aware that so much of the literature is unreliable.