The problem in my view, don't know what you think, is partially that AA is not talking directly to the engineer. Engineer escapes without demoing that the service is now working, and AA is not helping and supervising him.
However, there is more to it perhaps.
As I see it, sometimes small ISPs need to rent the services of an engineer. Other times they should be getting BT Wholesale to oversee and manage the entire job if the ISP is buying DSL from BT, which is the case here, as opposed to to just buying the use of a copper pair and that is all. Now here AA has ordered working good DSL from BT Wholesale yet AA is expected to oversee and fix the delivery of a service from BTW that AA has paid for and BTW is not doing anything, it is not ensuring that BTW’s customer AA gets the service that has been paid for.