The answer that was provided in April of 2009 is simply incorrect.
While the MTOE has both required and authorized columns, the required column comes from the TOE Level 1 (100% minimum mission essential wartime requirement for Soldiers and equipment). There may still be a few materiel items where the requirements on the MTOE are less than that of the TOE or that the materiel authorizations are less than the requirements, but it's a hangover from OEF/OIF days and will eventually be fixed. Army policy is that required equals authorized.
A TOE is strictly a requirements document. It is based on a doctrinal design from TRADOC. TRADOC designs organizations for capabilities needed in combat; therefore, TOEs/MTOES are strictly designed for combat. Any peacetime type functions are documented on a TDA of some sort.
MTOEs structured off the same TOE will vary according to the level of modernization (done by applying BOIPs), limited by the amount of modernized materiel we have to distribute and IAW units' priority.
Additional questions on this topic can be directed to David E. Retherford,