a. Yes. For the most-part, insurance companies follow the guidelines of the IICRC for mitigation services. However, they may not agree with industry best practices or agree with the technician actually conducting the mitigation (i.e., second guess his judgement).
b. Similar to health care insurance, your doctor may need to perform a certain operation or need to use a special type of equipment that your insurance company does not agree with, nor wants to pay for, and thus you must pay for that part.