It can depend on the delivery of the message. When I see a person wearing a Veterans cap, Ill make my way over to them, with a genuine smile and my hand out to shake theirs. I look them in the eye, thank them, and move on. If its a Vietnam Veteran, I add Welcome home. I keep it simple, straightforward, and in the manner of a private conversation.
When thanks are given to me, my response is, I appreciate that.
I agree totally with you. I am always pleasantly surprised when someone approaches me and thanks me for my service. And I always thank them for their thoughtfulness. Each time it happens, and it happens a lot in Tennessee, it warms my heart.