On the other hand, they still haven't quite grasped that proving a point can be a bit more complicated than lining up all the evidence they need to support it.
Don't get me wrong; failing to have enough evidence to prove that something can be true is still more likely to sink a given argument than almost anything else, and I certainly don't want anyone to think it's not worth their time to try. My goal in mentioning the above point is to remind people that a good argument has to account for all of the available evidence; using specific examples to prove a point only works if we have a good reason to believe those specific examples properly represent the entire body of evidence available. If there's silent evidence out there - something that's not being spotted because of poor sampling or confirmation bias - even a point that seems quite well supported can turn out to be quite wrong.
Some of the skeptic blogs I follow call this problem the toupee fallacy, after the specific example of trying to prove all toupees look fake by pointing out all the fake toupees one sees. It's fairly obvious that more realistic toupees will be excluded from those examples by default, since they won't be easily spotted, which creates the false impression that most toupees are fake.
The best way I know to avoid this problem is to carefully think about what counter arguments can be made against your argument, and actively look for evidence that might disprove your argument as well as evidence that can be used to prove it correct.