Thank you Wikipedia

Friends...our debate is solved. Read this exerpt from Wikipedia and rest assured that in the end we were ALL right.

"For many years, Big Bird was the only character on the show who saw him (he only came along when Big Bird was alone). The main adult characters teased Big Bird when he said he had seen the Snuffleupagus, because they didn't believe there was such an animal, often despite evidence to the contrary (such as an oversized teddy bear that Snuffy had left behind or segments in which Snuffy interacted with other characters, such as a street scene where Snuffy was seen playing London Bridge with some of the neighborhood kids). This was modeled in part on the imaginary friends some young children have.

By the late-1970s, the storylines had the adult characters becoming increasingly frustrated with Big Bird using Snuffleupagus as a scapegoat whenever something went wrong while they were out of the room. In one episode, newspapers on Sesame Street carried the front page headline, "Snuffy's got to go!"

Revelation

This running gag ended with the November 18, 1985 episode of Sesame Street, which was also episode 2096 and the 17th season premiere, when the adults finally met Snuffy. Big Bird is sick and tired of not having the grown-ups believing him when he tells them about Snuffy. So he decides to arrange for them to come to his nest when he yells the signaling word, "Food". When Big Bird calls out the word, Snuffy runs off to tell his mother about it, so once again the grown-ups just miss him. Gordon tells Big Bird he needs someone to help him keep Snuffy in his nest and Elmo offers to be the one. So when Snuffy returns, Elmo holds on to his snuffle so he can't go, Big Bird yells, "Food", and one by one the adults come and see Snuffy for the first time ever. After Snuffy introduces himself, Big Bird does an "I told you so" routine, prompting the adults to apologize profusely.

The Children's Television Workshop decided on this storyline largely after high-profile (and sometimes, graphic) stories on pedophilia and sexual abuse of children on shows such as 60 Minutes and 20/20. Concerns were raised that the running Snuffleupagus gag, where the adults refused to believe in Snuffleupagus despite Big Bird telling them about it and despite the fact that Snuffy had already been revealed to other Muppets, children, and even a few celebrity guest stars, could make children fear that they would similarly not be believed and therefore make them reluctant to tell an adult if they have been sexually abused."

So there you have it.