If a flight instructor, CFI or airport authority asked me for my documents, i have nothing to hide, i would willingly show them!
A "flight instructor, CFI" might be, but usually is not, responsible for the airfield.
If I land at PB84's strip, I'd see him or his representative as authorised to ask to see my pilot's licence. If we're both at Longside, it's none of his business.
If asked by someone, I'd first want to see their credentials.
Thread drift: about 60 years ago the story going round at Aberdeen Dyce was that the Airport Police had asked to see the licences of the BEA DC3 Pionair flight crew. As they were entitled to do, but it was an unprecedented occurrence.