Voa for US passport to Xiamen

Yes in theory, but nowadays it is not recommended to even try to travel by relying on Xiamen VOA. The reason is that the airport staff in the country from where you intend to travel to Xiamen are more than reluctant to allow you boarding when you declare something like this. Basically, you are advised to use 144 hour visa free transit by using a third country to enjoy 144 hour visa free transit and to be certain that you will be allowed boarding. For example, you can create your itinerary to look like this:

Hong Kong - Xiamen - Macau
Hong Kong - Xiamen - Taiwan

Also, those traveling to Xiamen have to know that even the short ride ferry to the nearby island of Kinmen (just in from of Xiamen) that belongs to Taiwan is an eligible option for 144 hour visa free transit. In other words, one can use Kinmen and be eligible for 144 hour visa free transit. For example:

Hong Kong - Xiamen - Kinmen (Taiwan)
Kinmen (Taiwan) - Xiamen - Hong Kong

Also, you can use 144 hour visa free transit to reach Kinmen and on your way back, you can rely on a Xiamen VOA because the Taiwanese authorities on Kinmen perfectly know that when you arrive by ship, then you will be definitely granted a VOA.

All you need is to book a ferry in advance, online and to have an e-confirmation for this ferry in hard copy (a printout).

So, there are solutions, but the solution should not be a Xiamen VOA when you arrive by plane!

My parents traveled from LAX to Xiamen, denied at origin saying they needed to purchase a ticket going to Macau.

They purchased the ticket, in hopes in getting a VOA, then to cancel the flight to Macau.

But even after arrival in Xiamen, they were told VOA is not possible and they still need to travel to Macau.

Originally they were going LAX-Xia-Tpe. Back to Taiwan.

But now they had to pay more and pay penalties to go LAX-Xiamen-Macau-Taiwan.

They said VOA doesn’t exist even IN XIAMEN AIRPORT. They all say you must travel to third country.

This is exactly as I have written:

"...nowadays it is not recommended to even try to travel by relying on Xiamen VOA."

Every trip to Xiamen if a visitor does not want to obtain a visa in advance should be done through visa free transit scheme. Xiamen VOA remains alive only for those arriving by sea.