Tell them that you haven't found documentary evidence and the difficulties in finding that evidence.
Sharing what you have found would go a long way, I think.
I often explain that many stories aren't supported by the math, as your high school administrator example proves.
Other times, it is because our family name is difficult to trace or I don't have an accurate version of the name they used before they came to the U.S.
Or I joke that that a story is hearsay, which which is inadmissible, your honor.
I have one of those "he was a rabbi" stories in my tree. But the evidence supports that he owned a barge and ferried goods across the Dneiper River.
He may have had aspirations to scholarship, or studied in his spare time.
Or it could have been his daughter embellishing because she wanted to make her family sound more important than it was.
My goal as a genealogist is to begin with hearsay; prove what I can, continue to search for what I can't.
The lack of documentary evidence from "the old country" for much of my family is frustrating. I can only hope that as more records are translated, something will pop up.
San Francisco, CA
SOSNA: Ivonivka (near Yampil), Mogilev
GOIKHMAN: Rascov, Mogilev
LEVIN: Vilna, Dnipro