Unless someone didn't put the wheel covers all the way on, what you say is next to impossible. On the inside of any rear wheel cover are 6 holes that cover the 6 lug nuts. With the lug nuts in those holes... The cover cannot rotate.
We were in the shop office when the shop guy said the thing about "wheel covers rotating" and the rig was in the parking lot with the covers inside. I wasn't sure about what was under the covers, but it sure looks like what you say is true. I'll do some trying on tomorrow and see how things are put together.
Our covers have several small metal spring tabs that are designed to secure the cover to the wheel. I slightly bent the tabs in a direction to resist slippage. In our case the right rear cover was slipping in a clockwise direction and counter clockwise on the left rear. I suspect the covers were slipping during braking but I am not sure. After about a 1,000 miles I can't detect any cover movement relative to the wheel. I can't really see how your covers are secured to the wheels so i am not sure if what I described has any relevance in your style covers.
In the third picture there are prongs sticking out of the holes in the cover's edge that should grip the rim.
We bought our PC used and the previous owner had put new tires and metal valve extensions on it last September. The extensions didn't reach far enough to use any TPMS sensors, so I asked this shop near us to replace them with longer extensions. Imagine my surprise when I removed one while adjusting a sensor and found they had just added a second short metal extension to the one already on the tire! Today we went back and all agreed they would redo the whole mess with one long extension on each tire that will reach outboard for easy access...at no additional cost to us. we will address the rotating wheel cover at that time. Thanks for you guys' input.