Does my son have to send a thank you note even though he said it at the time of the gift opening?

My husband and I were married in the same month of my sons birthday. My mother chose to give him his birthday gift at the wedding. After opening it, he promptly said "Thank You", and ran off to play with it. 3 weeks after the wedding, she called me to tell me she recieved the thank you note I sent her for the wedding gift. She then said to me that I needed to have my son write a thank you note for the birthday gift he recieved at that same time. I was then given a "motherly" lecture on teaching my children proper thank you note ettiquette. Being taken off guard, I was polite and quickly changed the subject. Not only do I feel that it was rude of her to insist on a thank you note for a gift she herself gave, but since my child thanked her on the spot, I still feel like he doesn't need to do this. What do you think? Should I go ahead and have my son write the note just to make her happy?