Check the original version, by Jim and Jesse (the tune was written by Jesse McReynolds). I don’t think it includes any extra beat. If the J&J version matches the way you play it, you might make a copy of it for Jim, and just let him know that's why you've been playing it that way. The person who wrote the tune chose to make it a certain way, and in bluegrass, the writer is given respect. See what Jim says, but if he's not moved, don't be too amazed, and you don't have to register an opinion, just say that's why you play it the way you play it.
You can both continue to play your different versions within the tune, and if the band follows you both, it's viable music -- but normally that's not done. Usually the person calling out the tune might even say: "and we're doing it in this particular way, though there are other ways to do it". Such protocol also applies on a few songs for which there are variant versions (such as, adding or not, an Em to Sitting on Top of the World, or a 1- or 3-beat pause in Worried Man Blues). Enough people know each version, it might be good practice to point out which version you’re doing, so no one will be surprised.
I agree with you about who should decide which version will be followed. Normally that would be the person who calls the tune, and that person would also be the one to start it. Jim is out of bounds in starting it without being invited. Chances are, Jim doesn't see it that way, and likes his version and doesn't want to have to change.
Good luck, and however it resolves, have fun jamming!