I think if my son topped out at 90 I could say he has touched 90. I don't have to see consistent 90 mph, to know 90 is something possible for that pitcher. Sure, the consistent 90 is better, but the one time 90 is very good.
also, from past experience I think some parents get confused rather than fibbing. We once had a dad complain about the top velocity we reported for his son. He claimed he saw our gun read 93 mph. Actually he did see that, but it was definitely the velocity off the bat. Seeing that we record every pitch, we explained that his son's fastball ranged from 82 to 85 and topped at 86 on one pitch. When this happens a pitch doesn't out of nowhere throw one 93. But dad saw it and thought his son threw one 93. BTW, this is something that happens more than you would think.
also, sometimes parents will ask someone with a radar gun what velocity they got on their son. This information is not always accurate, sometimes they give MPH of a different pitcher. Sometimes they just blurt out a number so they don't have to look it up. And sometimes the number is actually different than what we got.
Point is that parents are not always exaggerating. Sometimes they're just misinformed.