Why doesn't Peters find Dinosauria or Saurischia?

Peters has defended his amniote analysis as being superior to other published analyses, since it includes numerous genus-level OTUs.  And in this he is correct, though there are other measures of analysis quality too.  One obvious example is the number of characters.  There's no hard and fast rule regarding how many characters are needed to analyze a certain number of taxa, but you should at least include all characters previously utilized for the clade you're examining, unless some are invalid for whatever reason.  Peters' analysis has a large number of areas in which it differs not only from the consensus, but from any other proposed phylogeny.  One of these is his Dinosauria, which instead of the standard Ornithischia vs. Saurischia dichotomy, with the latter including Theropoda and Sauropodomorpha, has...

--Theropoda including Marasuchus, Herrerasaurus and Trialestes
--- Panphagia+Pampadromaeus
---- a clade of Pisanosaurus, poposaurs and silesaurids
----- Sauropodomorpha including Saturnalia, Thecodontosaurus and Massospondylus
------ Daemonosaurus + standard Ornithischia

Thus it has an equivalent of Phytodinosauria and includes a host of non-dinosaurian taxa.  Now, Saurischia is one of those clades (like Ornithothoraces) that while near-ubiquitous in published analyses, only takes a few extra steps to negate, so I'm not biased against it a priori.  And I've said half-seriously before that ornithischian-like silesaurids and theropod-like shuvosaurines and hallopodines could threaten dinosaurian monophyly.  Peters no doubt thinks his results are superior to the consensus, but did he actually test the consensus?  Let's see which saurischian and dinosaurian synapomorphies (based on only the unambiguous synapomorphies of Nesbitt, 2011) Peters included in his analysis.

Saurischia

Yes- (1) Subnarial foramen between the premaxilla-maxilla where the border of the foramen is present on both the maxilla and the premaxilla (12-1)*.
(12) Metacarpal IV shaft width significantly narrower than that of metacarpals I–III (261-1).
(13) Distal end of pubis expanded relative to the shaft (5 pubis boot) (283-1).

No- (2) Lacrimal folds over (5 overhangs) the posterior/posterodorsal part of the antorbital fenestra (38-1)*.
(3) Ventral ramus of the opisthotic covered by the lateralmost edge of exoccipital in posterior view (111-1). (4) Foramen in the ventral part of the splenial (165-1)*.
(5) Epipophyses present in posterior cervical vertebrae (cervicals 6–9) (187-1).
(6) Hyposphene- hypantrum accessory intervertebral articulations in the posterior cervical and/or dorsal vertebrae (195-1)*.
(7) First primordial sacral rib C-shaped in lateral view (209-1)*.
(8) Manual length accounts for more than 0.3 but less than 0.4 of the total length of humerus plus radius (247-1).
(9) Distal carpal V absent (249-1)*.
(10) Manual digit I, first phalanx (1.1) is the longest nonungual phalanx of the manus (253-1)*.
(11) Lateral distal condyle strongly distally expanded relative to medial condyle of metacarpal I (254-1).   (14) Cross section of the distal portion of the ischium subtriangular (293-2).
(15) Deep groove between the lateral condyle and crista tibiofibularis on the distal surface of the femur (322-1).
(16) Posterior prong of distal tarsal 4 pointed (350-1)*.
(17) Distal tarsal 4 with a distinct medial process present in the anteroposterior middle of the element (351-1)*.
(18) Astragalus, proximal surface possesses a marked rimmed and elliptical fossa posterior to the anterior ascending process (359-1)*.

Dinosauria

Yes- (7) Fourth trochanter a sharp flange (316-1)*.

No- (1) Exoccipitals do not meet along the midline on the floor of the endocranial cavity (115-1)*. Also in Crocodylomorpha and Effigia + Shuvosaurus.
(2) Supratemporal fossa present anterior to the supratemporal fenestra (144-1).
(3) Epipophyses present in postaxial anterior cervical vertebrae (186-0)*.
(4) Apex of deltopectoral crest situated at a point corresponding to more than 30% down the length of the
humerus (230-1)*.
(5) Radius shorter than 80% of humerus length (241-1).
(6) Proximal articular surfaces of the ischium with the ilium and the pubis separated by a large concave surface (297-2)*.
(8) Fourth trochanter asymmetrical, with distal margin forming a steeper angle to the shaft (317-1).
(9) Cnemial crest arcs anterolaterally (328-2)*.
(10) Distinct proximodistally oriented ridge present on the posterior face of the distal end of the tibia (336-1)*.
(11) Proximal articular facet for fibula of the astragalus occupies less than 0.3 of the transverse width of the element (362-1).
(12) Concave articular surface for the fibula of the calcaneum (378-2).

Wow!  Peters included 3 (17%) of saurischian characters and 1 (8%) of dinosaurian characters and didn't recover either clade?  Who'd have thunk?  In general, Peters' postcranial characters are few and usually reflect gross morphology.  Wanna know the humeral characters included?  Humerofemoral length and torsion.  The tibial ones?  Tibioilial length.  Distal tarsal characters?  None.  Peters is fond of saying his sister taxa "look similar", and this is why- the characters reflect a general morphotype.

There's a reason making an amniote analysis is so challenging.  It'd be easy enough to enter 300 taxa into Rieppel's or Mueller's analyses, but at that resolution, you need to add more characters to arrange taxa right within each subclade.  Peters has not done this, but I'd bet doing so, and defining his states better, would result in a more standard topology, albeit one that may have genuine surprises.