The provider wouldn't be accessing your equipment. But for you to configure it to allow for access to the DSL network. You may or not may not need to configure your wireless router to access the DSL network. The modem is normally their demarc, separating the customer's edge from the provider network. But for you to have access and now allow everyone to just jack into your RJ-11 outlet and get access to DSL, you may have to provide this PPPoE (or you may see PPPoDSL) password or id, etc.) for access.
Any troubleshooting they would do is only up to the Demarc on their end and the rest is your responsibility.