Is Southwest acting on a new policy?
I don't know whether Southwest or Jamaica has changed policy recently, but Southwest should be expected to treat someone who shows (only) a US passport as a US citizen. The Jamaican consulate in New York notes that visitors must "be in possession of a return or round trip ticket to another country to which they are admissible."
Now, a Jamaican immigration officer might recognize this traveler as a Jamaican citizen, but it's not reasonable to expect a relatively low-level employee of an airline to reach the same conclusion unless the traveler shows a Jamaican passport. Countries typically fine airlines when a passenger is refused entry unless the airline can show that the passenger presented adequate documents. The amount of the fine is typically in the range of a few thousand US dollars or equivalent. The lack of a round-trip ticket in this case leaves Southwest at risk of a fine.
The obvious advice for the traveler in question is to get a Jamaican passport. If she did in fact have and show a Jamaican passport in this case, then the advice would be to complain to Southwest and seek compensation.