SOCOM types can buy almost anything, what you're describing is a COTS purchase ("Commercial, Off The Shelf") or a semi-COTS without the usual gov't procurement channels, red tape, approvals, etc. It happens, but it doesn't make something 'mil spec' just because some unit buys some.
Mil spec means it was procured under a specification, the specs are controlled by some design agent or command, all components have pedigree & whatever lot traceability is called for in the contract. It usually means qualification testing, acceptance testing of a sample from each lot, and a ton of gov't rules and red tape.
Things that are truly "mil spec" and bought under a proper contract are different from things that some unit bought through a different procurement means.
Not sure if I'm helping answer your question, but that's my $0.02