Its not just Eddie... Meka is the same way
I take her to the monthly Yorkie Group meetups in our area and its always the same. When I put her down, the other pups are anxious to sniff her and play and she just doesnt want to be bothered
sometimes even snaps at them. And she always comes running back to me, wanting me to pick her up. I too, feel I must have done something wrong with her socializing skills. We didnt start the meet up groups until she was 1 yr and a half and I sometimes think that maybe we should have been doing it much earlier. I do envy the other dogs that go and play with eachother...for I have never seen her actually play with another dog.
Now people on the other hand, total different story. She goes crazy over anybody. Rolling and jumping around. Totally anxious to get their attention.