I believe the article's title is misleading - Danish foreign policy should have nothing to do with it. If the Danes didn't want to get caught up in our military adventures, they shouldn't have allowed one of their corporation's U.S. subsidiaries to bid on the ship maintenance work. Methinks this is just some EuroPress hand-wringing; it's not as though these ships - and their primary task - are a big secret.
Do a search on the Military Sealift Command - you'll find that they have an amazing number of ships squirreled away around the country. There are a few on the list that are of WWII vintage! The Fast Sealift ships are decidedly more modern, though. Here's a pic of one:
Haze grey and underway. Looks "Navy" to me.