There are indications that they are only secondarily anapsid.    From Wordnik.com.  [Drawing a Line in the Academic Sand - The Panda's Thumb] Reference

It doesnt seem likely that anapsid skulls are all secondarily derved from diapsids.    From Wordnik.com.  [Report on the 2005 Creation Mega Conference, Part Four - The Panda's Thumb] Reference

Mesasaurs were small crocodilian-like anapsid reptiles of about 300 million years ago.    From Wordnik.com.  [The Mosasaur and the missing link - The Panda's Thumb] Reference

Turtles were considered to be living anapsids although there was a significant temporal gap between the last anapsid reptile fossil and the first turtle fossil.    From Wordnik.com.  [Drawing a Line in the Academic Sand - The Panda's Thumb] Reference

This is where Lenny caustically suggested that I was a YEC for not knowing that turtles had been reclassified as diapsids with a secondarily anapsid appearing skull I hope that embryologically turtle skulls start off as diapsid and then change but I dont really know.    From Wordnik.com.  [Drawing a Line in the Academic Sand - The Panda's Thumb] Reference

Rental cars charlotte awhile for the swarthiness the apprehension of any azalea he has apraxic in a unmalleability or negligence anapsid, we are rectilineal at, bitingly, an nutrient huckster.    From Wordnik.com.  [Rational Review] Reference

Regardless; to continue with the idea that the basal reptile skull structure was initially felt to be anapsid and similar to that of lobe finned fishes and amphibians.    From Wordnik.com.  [Report on the 2005 Creation Mega Conference, Part Four - The Panda's Thumb] Reference

I think i’ve got this now: basal anapsid reptiles (which presumably gave rise to synapsid and sauropsid lineages) died out leaving no descendants. turtles, full diapsid reptiles closely allied to crocodiles, secondarily developed a seemingly (but not osteogenically identical) anapsid skull structure subsequently.    From Wordnik.com.  [Report on the 2005 Creation Mega Conference, Part Four - The Panda's Thumb] Reference