I'd rather not complain. I think what your MAA tried to say is that the LH fares from MAA to FLL are not valid for travel on US. This has nothting to do with interlining, but something with the marketing contracts between the airlines. I looked up a few of the published LH fares and they are all only allowing for UA and AC for segments within North America.

There is, like on most international routes, the exception of generic IATA fares, which are not carrier specific. It should be no problem to book a US segment under a IATA fare. But these fares are almost twice as expensive and therefore not really an option for most pax ...

The fact that carrier specific fares do not include all *A carriers is neither new, nor uncommon. Unless you travel on a *A RTW fare, you will most likely have some limitation because airlines simply do not negotiate all their fares with all their alliance partners.