First, let's go over the basic tests and conclusions of James and Pourtless' study. After making the almost correct observation that no published cladistic analysis has tested whether birds are dinosaurs (Senter 2004 did, but while the authors cite it they don't comment on it in that regard), James and Pourtless aim to correct this by constructing their own dataset with alternative proposed bird ancestors included. With basal archosauriforms as the outgroup, the authors also include crocodylomorphs, Longisquama, a few other pseudosuchians and numerous theropods. Running their dataset of 242 characters and 79 taxa, they recover a large number of MPTs. These are only ever illustrated as majority rule bootstrap trees after a posteriori pruning of taxa, and each alternative tree is basically a well supported Archosauria with a massive polytomy between crocodylomorphs, numerous theropod lineages and birds. Longisquama weakly (55% bootstrap) groups with birds if 21 "controversially homologous" characters (which are only coded for non-dinosaurs) are excluded and non-bird maniraptorans are pruned away. Statistical tests were done, seemingly showing the 'basal archosaur' (= Longisquama), crocodylomorph and dinosaur hypotheses of bird origins aren't any worse than each other.
|--Proterosuchus
`--+--Euparkeria
...`--+--Erythrosuchus
......`--+--Pseudosuchia(Ornithosuchus,Postosuchus,Crocodylotarsi)
.........|--Scleromochlus
.........|--Marasuchus
.........`--+--Eoraptor
............`--+--Herrerasaurus
...............|--Carnosauria("Syntarsus",Dilopho,Cerato,Sinraptor,Allo,Tyranno)
...............`--+--Juravenator
..................|--Sinosauropteryx
..................|--Compsognathus+Huaxiagnathus
..................|--Guanlong+Dilong
..................|--Effigia+Ornithomimosauria
..................|--Microvenator
..................`--+--Coelurus
.....................|--Ornitholestes
.....................|--Falcarius
.....................`--+--Therizinosauroidea
........................`--+--Oviraptorosauria+Dromaeosauridae
...........................`--+--Troodontidae
..............................`--+--Pelecanimimus+Avimimus+Parvicursorinae
.................................`--+--Caudipteryx
....................................`--+--Longisquama
.......................................`--Ornithes
Actual strict consensus of James and Pourtless' data, simplified so that genera which form monophyletic clades are represented by their clade names. Note no dinosaurs were coded for manual characters, Effigia is an ornithomimosaur, and Longisquama is deeply nested in Theropoda.
No, the biggest problem with James and Pourtless' analysis is that its matrix consists mostly of characters designed to diagnose coelurosaur clades (e.g. 96 from Clark et al.'s 2002 TWG analysis; 26 from Chiappe's 2002 bird analysis) plus those suggested by BANDits to group Longisquama and crocs with birds. So what happens when you analyze Longisquama in a coelurosaur/bird matrix after reconstructing its skull with theropod presumptions and pretending no dinosaur preserves hands? Given it doesn't preserve sacrum, pelvis, hindlimbs or tail, and that the vertebrae are basically uncodable, it emerges as a coelurosaur. When chatting with Nick Gardner about this I joked "I bet if you coded e.g. Coelurosauravus' front half into the matrix, it would be coelurosaurian too." So I coded Coelurosauravus' front half, the same parts preserved for Longisquama, and lo...
|--Proterosuchus
`--+--Euparkeria
...`--+--Erythrosuchus
......`--+--Pseudosuchia(Sclero,Ornithosu,Posto,Crocodylo)
.........`--+--Marasuchus
............`--+--Eoraptor
...............`--+--Herrerasaurus
..................`--+--Carnosauria("Syntarsus",Dilopho,Cerato,Sin,Allo,Tyranno)
.....................`--+--Compsognathidae
........................`--+--Guanlong+Dilong
...........................`--+--Microvenator
..............................`--+--Ornitholestes
.................................`--+--+--Coelurosauravus
....................................|..`--+--Effigia
....................................|.....`--Ornithomimo (inc. Pele,Longisquama)
....................................`--+--Coelurus
.......................................`--+--Falcarius
..........................................`--+--Therizinosauroidea
.............................................`--+--Ovirapt(inc.Caudi)+Dromaeo
................................................`--+--+--Troodontidae
...................................................|..`--Avimimus+Parvicursorinae
...................................................`--+--Sinovenator
......................................................`--Ornithes
I won my own bet. Interestingly, this tree also has a lot more resolution and details which agree with the consensus (e.g. Pelecanimimus in Ornithomimosauria, Caudipteryx in Oviraptorosauria), and Longisquama is moved from Avialae to Ornithomimosauria. Note Coelurosauravus is not thought by anyone to have anything to do with dinosaurs or birds, but still ends up as a maniraptoriform in James and Pourtless' matrix. This fairly neatly proves my idea that Longisquama could be a far more basal diapsid and still emerge as a coelurosaur. Note too that Longisquama is also an ornithomimosaur once the front half of Coelurosauravus is included, perhaps suggesting more signal between them than between Longisquama and birds.
So my conclusion is that very few characters were included that would support e.g. Tetanurae, Avepoda, Theropoda, Saurischia, Dinosauromorpha. Just enough are included to get a basically consensus phylogeny even without manual characters, though not enough to properly place Effigia or the front half of Coelurosauravus. The latter plus the theropodan assumptions in Longisquama's anatomy makes placement of thus genus particularly untrustworthy. Certainly, not enough characters were included to survive bootstrap analysis, where random characters are deleted or repeated and the analysis is rerun. It doesn't mean that "both the "early-archosaur" and "crocodylomorph" hypotheses are at least as well supported as the BMT [BAD] hypothesis", it means that James and Pourtless made a crappy analysis.
References- Evans and Haubold, 1987. A review of the Upper Permian genera Coelurosauravus, Weigeltisaurus and Gracilisaurus (Reptilia: Diapsida). Zoological Journal of the Linnean Society. 90(3), 275-303.
Hou, Martin, Zhou and Feduccia, 1996. Early adaptive radiation of birds: Evidence from fossils from Northeastern China. Science. 274, 1164-1167.
Senter, 2004. Phylogeny of the Drepanosauridae (Reptilia: Diapsida). Journal of Systematic Palaeontology. 2, 257-268.
Schaumberg, Unwin and Brandt, 2007. New information on the anatomy of the Late Permian gliding reptile Coelurosauravus. Palaontologische Zeitschrift. 81(2), 160-173.
James and Pourtless, 2009. Cladistics and the origin of birds: A review and two new analyses. Ornithological Monographs. 66, 78 pp.