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Looking at the functionality starting on page 32, this app sounds great. It looks like it grabs your points balance and figures out if you have enough points to book a specific flight, considering transfer partners and even credit card bonuses.
I could see why American wouldn't be happy with them, since it just uses them as a conduit for spending miles. I wonder if them simply not using the trademarks and arguing that it's the customers doing the logging in, and not them (so take it up with your customers) is enough to win the suit.