The fine points of the law (Trading with the Enemy Act, the Cuban Democracy Act of 1992 and the Helms-Burton Act of 1996) are that the prohibition is on doing business with Cuba. It applies to US citizens and resident aliens, and to US companies doing business anywhere in the world, including foreign subsiduaries. Basically a license is required prior to paying USD 1 to Cuba. So travel to Cuba is not prohibited, but paying for it by US companies is prohibited. This unambiguously covers a OWE ticket with AA segments that touches Cuba even if it is just a tech stop (and the LA flight isn't a tech stop). So AA is required to confiscate such a ticket when it is presented to AA (and is prohibited from selling such a ticket). Failure to do so has severe penalties. Given the scale of the penalties, and the small number of flights that touch Cuba, I would guess that the AA computer system is programmed to scan for all the flight numbers that violate the Cuba embargo. So I would say there is little scope for human error or discretion on what to do (most likely a high level supervisor over-ride is required, beyond the agent's capabilities).
The zeal with which the US govt enforces the embargo varies greatly. There was a big crackdown in 2003 for various reasons. Many Cuban-Americans in Florida visit Cuba each year, most in violation of the embargo, but they have the political clout to avoid any repercusions. The US govt tends to pick non-US citizens -- who do not have the right of appeal or voting power -- to make examples of. If you travel to Cuba and then enter the US, be prepared to show the country of purchase for every single item in your luggage; otherwise it will be deemed to have been bought in Cuba and confiscated. We all travel with original notarized receipts for all our clothes, don't we? In 2003 there was a famous case: US customs agents in Montreal would watch the pax exiting from the plane arriving from HVA and if they connected on to the US, they would get special treatment. The US customs inspection is done on US soil in Canada, but the HVA flight arrived on Canadian soil where the US agents had no right to observe the arriving pax. It was over the line, and doesn't currently happen, but it shows the seriousness of this particular "game".