When my kids were younger (younger than 13 or so) I had to be with them at Sam's Club, Costco & BJ's. I was startled the first time it happened, but the vendor politely explained that they needed the parents permission first. They didn't explain why, but it hadn't occurred to me until that moment that maybe kids ran around grabbing samples or maybe they were concerned about allergic reactions.
My kids are 17 & 15 and no denies them samples now if they ask for it.
Off-topic a bit but it still tickles me:
I was at Sam's Club in Erie, PA with my kids, DH & MIL. My kids asked if they could grab a sample of something and I reminded them, maybe a bit sternly, to remember to say 'please' and 'thank you'. They came back with their sample while I was chatting with my MIL about something, when an older lady came up to me and asked, "Are these your children?" pointing to my two rugrats.
(My MIL was hysterical with laughter because I verrrrrrry hesitatingly said, "...uh...yes?")
The older lady said to me, a little sternly, "I just wanted you to know they said 'please' and 'thank you' and were very polite to the sample vendor!"
Me (meekly): Oh...thanks for letting me know.