Does USAREC really check credit and DTI?

Of course.

If you don't have any delinquent debt, you should be fine. Delinquent debt is an issue for things like recruiting or security clearances. People who regularly are working to pay off their debt isn't an issue.

It isn't uncommon for any Command to run financials on their people. Especially if you hold an elevated clearance or have a position that is considered high vis. That is standard SOP to identify anyone who can be exploited.