Personally I don't think that someone who gets two wins and one second place should only be 4 points ahead of someone who gets only one win and a finish outside of the podium isn't exactly fair. It's more exciting sure, but one dnf from the leader and it's almost impossible for him to get back up to the top. Even if you are the best driver in your group if you get unlucky with a bad race or two, and the other top drivers don't, you are have absolutely no chance in catching up.
That's what I mean when I say a linear point system rewards consistency but it's not hard to disprove your example if you'd like me to. Even with an FIA style points system and no drops, a couple of bad races will probably still sink you for the championship because the winning driver, who would normally have finished second to you, will get 25 points for the win. So lets take an example:
Let's say there are 6 races and you would win every single race if you finished, but bad luck gives you a couple of tenth places and 4 wins. Your nearest competitor runs second and finishes every race, but wins the two that you finished poorly in.
With a straightline points system:
Him: 94 points. He wins.
You: 78 points. You lose.
With the FIA's point system:
Him: 122 points. He wins.
You: 102 points. You lose.
Same results either way. Even if you had 4 firsts, one second and a tenth place, and your opponent was more consistent with only 2 firsts but 4 seconds, he'd still win by 3 points under the FIA system. Under either system consistency is always the key to winning, especially in a very short series and it's only under a rare set of circumstances that the two systems would provide different winners.
Having said that, an easy fix for this is to allow a dropped race or two for your worst finishes, which is very common in online racing, at least in GT5/6.
IMO you create a points system primarily to encourage participation and provide close competition. It's just as important, perhaps more important, that those competing for 4th through 16th feel like they have someone close to them in the points tally to compete with. Everyone is racing their own race, and to have a competitor near you on the track that you are close to in points is what exciting racing is all about and encourages people to continue to see the series through to the end. Declining participation due to demotivated racers is the bane of online racing. Overall
"fairness", whatever that means in this context, is secondary at best, again, IMO.