Please feel free to tell me why my interpretation is wrong. I understand stats just well enough to get myself in trouble.
The line for actual ability is basically x=y. If you scored 10%, you're in the bottom quartile. If you scored 100%, you're in the top quartile. That line isn't really data, just something for comparison. The perceived ability line is the one that utilizes the data. It seems to show that once you average out what everyone rated themselves, it ends up kind of in the middle between ~55-70%. So the people who scored 10% assumed, on average, they would score around 55%. The people who scored 100% assumed, on average, that they would score about 75%. That makes the average expected score much higher than the actual score on the low end and somewhat lower than the actual score on the high end.
I'd interpret this as the bottom quartile thinks they're average and the top quartile thinks they're a bit above average. So basically everyone thinks they're average-ish, but the people who did worst on the test were the most wrong about that. But then again, I can't remember what the questions on the test were even about and just the single graph isn't terribly useful to argue over because it's missing all of the context of the paper.
Now that I've sat and interpreted the graph using my own set of notions about what the numbers mean and what the graph actually shows, I feel like this ought to be used as one of those life lessons about how quotes and diagrams outside of their context within a paper are the epitome of the phrase "lies, damn lies, and statistics." Statistics aren't always lies, but they're incredibly easy to bend to your own biases and assumptions.