Why should we expect there isn't a correlation? They do mention it in their analysis. At the end of the day, just because there might be a systematic bias in your result doesn't mean there is a systematic bias.

All real-world analysis (especially for observational studies) rests on certain assumptions. It is always true that these assumptions might be wrong, but it is important to think about whether or not the assumption is plausible. It seems plausible that on average, a lawyer who is able to get better outcomes when they don't settle is also able to get better outcomes when they do settle.

Furthermore, even if most cases are settled, the rare cases that do go to trial can have an outsized impact. Usually people settle because a bad judgment is devastating (as well as not wanting to pay legal costs).