Fish, RPI has MAJOR design flaws. Let's take your Illinois example. Note that Illinois is 19-0 and Kansas/Duke at 1/2 are both 14-0. If you simply dropped off of their schedule and record Illinois' 5 weakest opponents in terms of SOS I am confident you would see them with a much higher SOS and in turn a much higher ranking.
Think about that for a minute (maybe for you, around 15 seconds) and you'll note where the flaw is.
Why should a team be punished lower for winning 5 extra games (by large margins, mind you) against low-rated teams and another team be rewarded for playing less games and not playing those low-rated teams in 5 extra games? If Illinois hadn't played those 5 lowest teams, which were all whipped, how would that show them to be a better teams. It wouldn't, of course. But that's exactly what the RPI does!
The SOS is just poorly designed when it comes to comparing teams with a different number of played games. Look closely and you'll see only Wake has played more "1-50" teams and is 7-1; Illinois 7-0. Duke/Kansas both 5-0 vs. 1-50 teams. Illinois is undefeated and has 5 more wins overall and 2 more wins over top 50 clubs than both Kansas and Duke.
One would assume a widely-used index like RPI is well done, but alas it is not necessarily so. However, I will say that by the season is done some of these design flaws are less noticable and relevant -- and I suppose RPI is meant to be used at the end of the season. Nonetheless, RPI is flawed, even for what it is specifically trying to gauge.