I would think the curved appearance of the 12 inch wide tire is just that, an appearance.
The tires are made out of rubber, and from a function point of view, doesn't the tire flex, and result in a flat contact patch??
Then, it is possible, that mounting a 12 inch wide tire on a 12 inch wide rim REDUCES traction!!
If the rim is too wide, there is no support for the center of the tread.
This has always been an issue with bias ply tires, a very common issue in the 1960's IIRC,,,,