these guys service a lot of Ac's for different companies. the thing is taking AMC officially through the company means it is their duty to see if you get a good servicing & maintainence. Imagine you do it independently with a servicing agency and the servicing guy breaks a part of your AC and does something which creates problems in your AC... then you have to catch hold of the agency.
The same thing if taken from the AC company, you go after the company and see that your AC is replaced or fixed.