https://ls1tech.com/forums/cadillac-...alignment.html
As you see in the picture from above link, wider tire (even with properly wider rim) does not necessarily have bigger contact patch.
It just changes the shape of contact patch. (elongated more on sideway)
Contact patch area is solely function of weight of the car and tire pressure. (within reasonable tire width of course. not talking about bicycle tire like width)
As mentioned above, proper rim witch is for optimal sidewall support.
The Tirerack article just says 'tire width' not 'contact patch'.