I agree that having a political op-ed published in a major newspaper is evidence that you understand politics, I don't think it's tremendously strong evidence

I agree it's not tremendously strong evidence. Having multiple op-eds published in multiple papers, as I have, provides more evidence, of course.

If you write something that will appeal to the paper's readers, or that will arouse controversy and draw in readers (or, online, clicks on advertisements), then that may be all they care about. There is some pretty stupid stuff published in major newspapers.

Yup, there is stupid stuff, but it's most often by specific writers who they know and specifically frame as controversial, for example a prisoner on a hunger strike in California. They generally don't publish stupid stuff by people who are positioned as experts. Papers do have a reputation to uphold.