In this case, no.
I was visiting friends this past weekend, and one of them said something about my prescription pills, and I thanked her for the reminder: but this is a very close friend, with whom I have discussed my health, and I had the pill container out in the open (rather than tucked away in my bag). I wouldn't appreciate random acquaintances asking if I am taking my medicine properly, or whether/how recently I've had some medical test, and my friend knew that. Nonetheless, after taking the medicine I thanked her and reiterated that I appreciated the reminder, rather than feeling nagged.