This comes up sometimes in documentaries, books, etc. People forget about the Muppeteers there and just believe in the characters totally without thinking about it. Guest stars on the Muppet Show have noted it. Carol Burnett said once: "When Kermit is up there, staring you in the face, you believe in him completely. I feel that Kermit has a soul. As for Animal, I had to dance with Animal and I had no difficulty in believing in him either because I was
terrified of Animal!"
Kevin Clash mentioned that kids just see the Muppeteers as "people who carry their friends around". In one of the Fraggle Rock DVDs, people forget that the voices behind the Gorgs are off set (with those mitten things). Scripts were sometimes given to the Gorgs instead of Jerry, Cheryl and Richard!
Do you have Caroll Spinney's book? There's a beautiful scene with Big Bird and Snuffy where they say goodbye (supposedly) forever. I don't want to spoil the story if you haven't read it, but you should. I think you'd like it. It deals with this, too.
So I don't think you're alone in just enjoying the characters and forgetting about the Muppeteers. Lots of people do it...guest stars, adults, even Muppeteers!
You may want to check this clip out, too. I often forget that it's Caroll in this clip and just listen to what Big Bird says:
http://www.youtube.com/watch?v=S4gydgBIpf0
Convincing John