Sounds like complete Central America wild west made up nonsense.
Bags get lost all the time, I've never heard of a GA threatening to deny boarding because the airline didn't transfer a bag correctly between flights.
No idea what email address they told you, but when you get back to LHR, just file a lost bag report with the AA baggage office there (assuming your bag doesn't make it). Forget about emailing or whatever the GA said about not sending your bag on, what are they going to do just hold it there?!
Out of curiosity what email did they give you?
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