I have noted that the ‘store brand’ of oil at the major chains is generally re-refined (recycled) oil. I am guessing that the mechanic assumes that they use their store brand for oil changes. Seems a reasonable assumption in the absence of any actual information.
Yes, the military does use recycled oil for some applications. At least the Air Force does. I consult for them doing computer work and I see the purchase records. I don’t know what they use it for, but they buy it.
I would say that if the oil service code meets the requirement of your car manufacturer, it should be just fine. I still would not use it unless I could not get anything else, but that’s just my irrational response where my car is concerned.