All commercial bottle-necked brass is heat treated before loading. It is an essential step of ammo manufacture and helps assure proper bullet pull and absence of neck cracking during storage. The biggest difference is that on commercial brass, the rainbow heat treating colors are polished off in a subsequent operation, while the MIL-SPEC requires that the heat treating colors remain as proof of the heat treating step.
Lake City and other arsenals certainly makes good military brass, and is probably the most commonly found. However, ALL of the commercial manufacturers at one time or another have produced MIL-SPEC 5.56x45 NATO for Government use, and they are all required to meet the military specifications. For that matter, almost all foreign military production of 5.56x45 NATO caliber was originally produced on US supplied equipment and made to US MIL-SPEC, including that produced in korea, taiwan, singapore, the philipines, etc. Quality control has fluctuated at times, but all of these producers were brought under the umbrella of US military-industrial technical assistance.