That's not correct; one PNR can contain multiple tickets. Further, there's a specific exception to the "no through-checking bags on separate tickets" for situations involving both an AA award ticket and an AA revenue ticket; however, these must both be reflected on a single PNR. The only way to do this is to call AA and get a knowledgable agent.

However, your general point as a good one--since you have to collect bags in MIA anyway, there's not much advantage in through-checking in this situation. Just have them tag the bags again at the bag drop for the MIA->IAH ticket.