I am not positive but I ve had a male betta jump from one section of hs tank into another (over tei divider) and he fought with the other on right up untill I caught them one has big red blotch on head and both no more pretty longish halfmoon looking fins, I think they woulda kept fighting if I didnt catch them It was small though, I dunno bout big tank, but I would think unless they were on two ends and did not see eachother they would fight.
Also that is a good theory also, same with africans they dont get along unless they have an equlaibrium of a certian amount, maybe bettas work like that also?