Even if true, as I say they could still draw the top and bottom of the scenes without affecting that horizontal FOV.
That's aspect ratio. They are projected onto a wider screen because human vision has a slightly wider FOV than vertical, plus there's nothing of interest to focus on in the sky or at our feet so those spaces are more filtered, hence the wide screen is a more natural fit.
FOV is how many degrees around a person they can see. This FOV is generated within the game by rendering options. See
here. That FOV can then be cropped to any aspect as the window into that scene. Taking those BF3 examples just linked to, you could add borders top and bottom to make the aspect more widescreen, without changing the horizontal FOV, but of course reducing the vertical FOV.
Ergo, you don't need a wide screen aspect to accommodate a wider FOV. In a typical scene though, a wider FOV will just fill the sky and ground with boringness, which doesn't make for good viewing. The 90 degree example above has a lot of wasted space top and bottom. Cropping to the relevant band of detail in the centre makes sense both artistically and technically. I've heard PC gamers talk of the annoyance of 1080p/16:9 monitors as it restricts their vertical FOV and for some games that's definitely a disadvantage.