If feather bed
is a bed with a feather mattress or the feather mattress alone, feather bed
are false friends and the entry is wrong.
As a matter of fact, the German Federbett has always been a quilt. Personally, I don't use the word, I say "Daunendecke" (no matter whether it contains downs or feathers or both) and AFAIK Daunendecke is also used in the "Princess and the Pea" ("Bett aus 20 Matratzen und darüber 20 Daunendecken/Eiderdaunendecken").
Interestingly enough, I found descriptions of the fairy tale on the Web (English domains) saying "a bed with 20 mattresses and 20 feather-beds" (i.e. a feather-bed is not a mattress, but an eiderdown), so maybe "feather bed" can have two meanings in common usage or the dictionary definitions quoted are wrong.
One of the examples at oxforddictionaries.com (see #0) is a quotation from here:
With the lighting taking care of, let's move to the next immediate need – a down comforter, of course. ... If your client prefers a slightly crisp sleeping temperature on cold wintry nights, allow the down comforter to provide the warmth. Another option is a fluffy feather bed that adds some extra cushion to the mattress and some warmth to the nighttime. Place the feather bed either under the fitted sheet or above it with the cover over it.
Pictures and shopping sites also point to a cover rather than to a mattress:
I wonder if you can have a restful night's sleep on a soft mattress stuffed with feathers at all. Wouldn't that be murder on your back?
Should feather bed turn out to be a quilt, then the entry doesn't need any correction, just an explanatory note.