Does Confuciusornis really have a skull configuration like juvenile Alligator?

EDIT: The issues have been resolved.  The short version is that the wireframes are not actually of the specimens, but rather what the average specimen with that same gross skull shape and the minor variables that correlate with it would look like.  The long version is here.

Bhullar et al. (2012) have a recent paper that is getting a lot of press.  Its thesis is that bird skulls resemble those of juvenile theropods, and I agree.  I do have a problem with one of their figures though, showing how juvenile Alligator and Confuciusornis supposedly have an almost identical skull configuration.  First I wondered why use Confuciusornis, as it has a skull which is "very unusual for basal birds, with its robust construction, highly reduced antorbital area, etc.".  I commented on this at Jaime's blog, and Bhullar replied there that "Confuciusornis was just one example; we could as easily have used one of the enantiornithines, for instance, and the skulls would have been almost as similar. The early avialans in general cluster with the juvenile/embryonic archosaurs. Moreover, apart from the premaxilla, which is a very separate developmental module derived from a different embryonic primordium and patterned by different genes, Confuciusornis does _not_ have an especially reduced antorbital region compared to other early avialans. Rather, it’s square in the middle, shorter than Archaeopteryx and similar to a juvenile enantiornithine."  Being skeptical, I made my own wireframes...

Bhullar et al.'s figure 4, with Confuciusornis and nearly identical juvenile Alligator outlines on the right.

Bhullar et al. used Confuciusornis specimen GMV-2132, which is a good choice as it is largely uncrushed and articulated, except for a posteriorly displaced lacrimal.  It can be seen in figure 10 of Chiappe et al. (1999).  Here's my attempt at making a wireframe based on the landmarks Bhullar et al. used.

Er... doesn't really look the same, does it?  Below are the wireframe superimposed on the skull (which has only been altered by moving the lacrimal forward, and erasing fragments that were in the orbit and naris), plus figure S1 from their paper to show the landmarks used, so you can judge my accuracy for yourself.  Some points had to be estimated, while others such as those involving the prefrontal don't exist in Confuciusornis.

Here's the closest fit I could get between Bhullar et al.'s wireframe and the skull.  So now my big concern is how Bhullar et al. even got their data.

The beak isn't even close, being too blunt with a tiny anteriorly positioned naris and anteriorly placed antorbital fenestra, while the braincase is too posterodorsally expanded.

Further, Bhullar claimed the juvenile enantiornithine would be almost as similar, and that its antorbital region is similar to Confuciusornis besides the premaxilla.  The enantiornithine in question is LP-4450-IEI, described by Sanz et al. (1997), whose reconstruction Bhullar et al. used for their wireframe.  Below is my attempt (Confuciusornis on the left, LP-4450-IEI on thr right), again with an overlay of figure 3C from Sanz et al. so you can judge the accuracy for yourself.  Notice that even ignoring the premaxilla, Confuciusornis has very short nasals and antorbital fenestra, a small, vertical and posteriorly placed ascending maxillary process (which is possibly all the medial wall of the antorbital fossa, making it even more dissimilar to the enantiornithine which preserves no medial wall), and no anterior lacrimal process, all of which show up in my wireframes.  I've also included Bhullar et al.'s version from their figure 3E, and I honestly don't see how they got it.

Here's the closest overlay of their wireframe with the skull I could manage-

The premaxilla is way too long, the snout decurved, the dorsal jugal process sitting in the orbit, they attached a point to the tip of the pterygoid/orbital process of the quadrate (which is not one of their points, as seen on Herrerasaurus), the naris is tiny, the squamosal is given a large ventral process...  What happened?!

I think the above comparisons show that Bhullar et al.'s data is seriously flawed.  Originally I was just questioning the use of Confuciusornis, but now I see that the wireframes don't even fit the skull.  Just comparing Confuciusornis with their juvenile Alligator (figure 1b) shows the wireframes couldn't possibly be that similar-

At the very least, there are three external naris landmarks, and Alligator's is small and anteriorly placed, while Confuciusornis' is huge and mostly at the level of Alligator's lacrimal.  Or how about the seven laterotemporal fenestra landmarks, considering Alligator's anteriorly placed weird crurotarsan fenestra with the anteriorly projected quadratojugal?  How did Bhullar et al. ever get this amount of overlap?!

I've emailed Bhullar with a link to this page, so hopefully there will be a response.

References- Sanz, Chiappe, Perez-Moreno, Moratalla, Hernandez-Carrasquilla, Buscalioni, Ortega, Poyato-Ariza, Rasskin-Gutman and Martinez-Delclos, 1997. A nestling bird from the Lower Cretaceous of Spain: Implications for avian skull and neck evolution. Science. 276, 1543-1546.

Chiappe, Ji, Ji and Norell, 1999. Anatomy and systematics of the Confuciusornithidae (Theropoda: Aves) from the Late Mesozoic of Northeastern China. Bulletin of American Museum of Natural History. 242, 1-89.

Bhullar, Marugán-Lobón, Racimo, Bever, Rowe and Norell, 2012. Birds have paedomorphic skulls. Nature. 487, 223-226.