Interlining has zero to do with acommodating on other carriers' flights. It's simply more tedious and expensive for the carrier and thus a last resort. Interlining has to do with baggage. Acommodating has to do with agreements by which carriers accept each others tickets at the price paid for the segment(s) under the theory that it all evens out.

Generally carriers try to rebook: 1) On their own metal; 2) within alliance; 3) other carrier (a last ditch). When the other carrier is one such as B6, it means that AA is actually buying a ticket in the customer's name on AA's own account. This is doable for AA because B6 fares are often low and thus, depending on the value of the rerouted segment, AA may break even or close to it.

In the end, it's all in the CSR's discretion so it really pays to be nice about these situations and to be fully prepared with the alternatives which you seek. The easier you make it for the CSR, the more likely that you get it.