Neither of your links contain an actual correlation measure, or links to actual source data. To even call them "articles" is a stretch, they appear to essentially be ads / link magnets (which as a category have an obvious bias).

You have to like, control for things and stuff..

I'm not familar with Fed notes, is there an actual published study behind that Fed note?

The amount of data and studies out there to correlate income level and credit rating is surprisingly low. The data set used by the Fed seems surprisingly weak, a self-reported survey sent out with credit card offers:

We use the Mintel/Comperemedia data (the Mintel data henceforth) that provide a unique combination of credit scores and survey-based income data for the same consumers. The Mintel data set is a monthly proprietary survey of credit card offers, with about 2,500 consumers selected to participate in the survey each month. Participants of the Mintel survey have very similar educational attainments and income to other nationwide representative household surveys, such as the Survey of Consumer Finances. The Mintel sample, however, has a somewhat higher average age and greater share of white consumers.

The link literally is a published study. Not sure if that's supposed to be some kind of gotcha. Fed research generally isn't published in third party journals.

And the method you describe isn't weak at all, compared to social sciences research in general. If anything, it's stronger than most could possibly be, since lying on the survey is a crime in this case.

I just expected a little more information around their data source other than "It's hard to find good data, this proprietary source (so you can't look at it) is the best we could find, it has some known biases, but we eyeballed it and it looks good enough". In particular I was looking for a full study that explained what "very similar" meant since the fairness of that input data seems it's key to their results.

if true, that doesn't look like a very strong correlation to me, at least at first blush. the difference between high and low income is 111 points on a scale that goes from 300 to 850?

In terms of getting a loan, anything below 580 is considered "very poor" (though I don't now how FICO relates to car insurance pricing). So the usable range if you're looking for good rates is more like 580-850, or 270 points.