When dealing with the sizes of rifle scopes, this line is pretty much true. A larger objective lens gives you more field of view, not a brighter image.
The two are inseparable. The larger the objective lens, the more light. The limitation is in restricting the amount of light that can be passed to the lens as in a hood or tube extension prior to the objective. You gain a larger FOV by increasing the degree of arc to the lens, that way you can reduce the tube diameter, but with this you run the risk of increased vignetting or distortion.