Correct!

What's a MAC and what do they do? A Medicare Administrative Contractor (MAC) is a private health care insurer that has been awarded a geographic jurisdiction to process Medicare Part A and Part B (A/B) medical claims or Durable Medical Equipment (DME) claims for Medicare Fee-For-Service (FFS) beneficiaries. CMS relies on a network of MACs to serve as the primary operational contact between the Medicare FFS program and the health care providers enrolled in the program. MACs are multi-state, regional contractors responsible for administering both Medicare Part A and Medicare Part B claims. MACs perform many activities including:

Process Medicare FFS claims Make and account for Medicare FFS payments Enroll providers in the Medicare FFS program Handle provider reimbursement services and audit institutional provider cost reports Handle redetermination requests (1st stage appeals process) Respond to provider inquiries Educate providers about Medicare FFS billing requirements Establish local coverage determinations (LCD’s) Review medical records for selected claims Coordinate with CMS and other FFS contractors

ETA; Wrt military private contractors, they used to be called "mercenaries." Iirc, Rene Descarte was, so make of that what you will.