Does USAREC really check credit and DTI?

Of course.

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.

Yes. Any command can run this and it is normal in cases of security clearance positions above secret and any position of real authority. This is to insure that you are not a risk and cannot be exploited by a foreign or even local influence.

As long as you are not seriously delinquent, are paying your debt down or are actively managing it you are fine.