I was unable to find my original reference, but while there is a definite tilt toward lower-income groups in the military, it isn't as sharp as I was led to believe. I don't remember if they divided the statistics between enlisted and officers, which would be an important piece of information.

The division between officers and enlisted is a definite line. About 10 percent of enlisted men have completed college, as opposed to well over 90 percent of officers. Don't know how that breaks down as far as income background goes, but an good educated guess would be that, as you say, more enlisted men come from lower-income backgrounds than officers.