I thought the Brotherhood developed the T-60 on their own between the events of Fallout 3 and 4.
T60 is meant to be a specialised variant in use by airborne units, IIRC. Even so, it could simply be advanced enough (IE designed to go into a mass production cycle after 2077) that it never saw widespread use before the nukes, like the Vertibird chopper.Adams AFB was known to have developed Eyebots (or worked on them), Hellfire armour and (presumably) some more other stuff like that, so it's not unfeasible the Brotherhood found the caches of these suits when salvaging Adams. But it is said to be designed by the US military. It was likely just never all that widespread before the war, with T51 and T45 making up the majority of the US forces.Alternatively, it could have been a variant designed for US soldiers in the Gobi Campaign. Would make sense.