I don't think both teams use the exact same feed. I think most if not all stadiums have multiple CF cameras, right next to each other, specifically for each team to have its own feed. They probably use single cameras at most other points in the stadium (except maybe the camera wells right next to the dugouts), but I believe each truck has access to the single cameras in case, for instance, the visiting director wants to show a closeup on a particular visiting player they are talking about, or want to show a fan in the stands wearing visiting team gear.