Yes this is basically the reason. Those countries need USD to buy american products.
If they exchange the dollars with the euro then someone in the EU will end up with those dollars and that person can't do anything but buy US products.
Ever heard of Eurodollars? That’s exactly what the original article is talking about. There are foreign banks that loan dollars—fractionally—outside of the US banking system. Dollars are needed to settle those debts, and they exist fully outside of the US.
If they exchange the dollars with the euro then someone in the EU will end up with those dollars and that person can't do anything but buy US products.