Expectations are always so high for big things like this-that the real meeting probably could never have lived up to them. They were expecting I think to meet the scruffy, greasy, rocker from 55 who was on fire and they met a man of 30 who was at this point beyond that. Everything they were doing he had done, before them. He probably did feel like he was forced into meeting them-but tried to make the best of it.
They always kept a respect for Elvis and his talent IMO- John wanted Elvis to be at his Toronto Peace Festival in 69, George wanted Elvis to be featured in "the Traveling Wilburys" in the 80s and even asked Priscilla and the estate for some recording by Elvis which could be used to build a song by the group-George later decided it was kind of morbid to try to do so.(although after Roy Orbison died they built a video from one of the recordings which showed a guitar in a rocking chair when Orbisons vocal part played so I guess he changed his mind)
If you asked any of the Beatles if they would have rather not met Elvis-I'm sure they would have said- no we're were glad we did.