Welcome to FT.
First, yes, they can do this, as you surmised.
Second-have you looked at any options with connections? Maybe something works better that is not direct. AA have shown general willingness to work with people,but only if there are actual options.
If there are no options, there's not much they can do.You do have an option to get a refund,but that won't help you.
What about leaving the next day?
Cheers.