This is exactly correct. Not only are individuals not their customers, lenders actively profit when credit reports are worse than they should be, and these profits support the reporting agencies directly.
It is the exact same scam as the ratings agencies passing off sub-prime mortgages as AAA. And it is completely due to the fact that the entire industry is supported by taxpayer money; financial institutions that fail to assess risk correctly are prevented from failing.
Actually, it's extremely different. In the mortgage case, risk was assessed as lower than it actually is when making loans. The normal market mechanism for correction is that such lenders lose money and eventually go bankrupt, so it's perfectly coherent to claim that being backstopped by the taxpayers distorts the correction. Note that this correction doesn't rely on the lenders having competition -- if the entire industry is making loans below the cost of risk it will still lose money. Also note that the loss of money was absolute. They loans were not merely less profitable than they could be, they lost money on net.
In contrast, if you assess risk as higher than it actually is, you still make profit, albeit perhaps less than otherwise. The normal market mechanism for correction is not bankruptcy, but competition. There are no losses for taxpayers to backstop. Of course, in theory lenders could eventually lose all their customers to other lenders using a more accurate model of consumers, but that isn't happening; and if it is due to government distortion it's not the same mechanism at all as propping up failing institutions.
I suspect the real situation is this:
Credit reporting agencies provide mostly accurate information. If I'm a lender, I want accurate information. If agency A offers "lender-friendly" bad credit reports and agency B offers accurate reports, I can steal from lenders using agency A all the customers who have have falsely bad reports from agency A. Your claim that providing bad credit reports helps lenders is only true if the interest rate for any given credit rating is fixed by law or something.
Nevertheless, "mostly accurate" could easily allow for a lot of anecdotes of inaccuracy. The natural barriers to entry for a CRA are extremely high, so a tiny fraction of consumers with inaccurate accounts will not cause a competitor to spring up, but a tiny fraction could still be a large absolute number of consumers.