The evidence is to the contrary--middle class and above are over-represented in the US military.

"Their median family income is more than $73,000, compared with $66,000 for civilians, and recruits are most likely to come from families in the middle of the wealth distribution, with median wealth of $87,000, almost $10,000 more than civilians."

This is for enlisted members. It's probably safe to have some intuition that officers will skew wealthier.

In the UK it’s pretty common for wealthy upper-class people to do a few years in the Army before they take over the family business.