That's not true, they can and do. They appear as tiny white spots on the smooth black plastic of my coops, and they are sufficiently well glued on that a simple wipe doesn't get them off; I have to use either the jet wash or a plastic scourer (the sort for getting detritus off pots and pans; works well on all surfaces without leaving scratches I've found) with vinegar-spiked water.
I have completely disassembled two of the coops this summer to tackle them, but I haven't done all four simultaneously to avoid disturbing broodies or layers, and since they are all close together and the flock change their sleeping arrangements all the time (and I think the info in BDutch's Dutch site link was correct, that they can and do travel on the birds themselves as well, even though they don't live on them as such), they are reinfected sooner or later.
The advantage with the Nestera coops is that they can be fully disassembled into single flat sheets, so all joins and corners can be opened up and exposed if a thorough job is needed. And even for a quicky holding operation, the sheets are easy to clean of visible mite eggs, and with water rather than nasty or expensive chemicals, essentially.
As it happens I have a photo in which you can see the mite eggs:
View attachment 3922629
They are the little white dots scattered all over on the black plastic.