When changing out the tires yesterday, I decided to take some pictures of the Rivals versus Continental DW, etc.
First up is 245 Rival versus 245 DW, both on 8.5" wheels (these are actually 245/40-18 Rival vs 245/35-19 DW):

Here's a look at the difference in mounted section width -- the Rival measured 11mm wider than the DW:

Next up is a real shocker, to me at least -- both of these are 245 Rivals, one on an 8.5" wheel and the other on a 9.5" wheel:

I said shocker since the "rule of thumb" is supposedly, quoting TireRack here:
The industry rule of thumb is that for every 1/2" change in rim width, the tire's section width will correspondingly change by approximately 2/10". I measured the section width difference at 24mm (i.e. instead of 0.4" or 10mm):

Last up is a 265 DW vs 245 Rival, both on 9.5" wheels (265/35-19 DW, 245/40-18 Rival):

The 265 DW measured out 8mm wider than the 245 Rival:

Still super happy with the Rivals so far.