Summary for those just skimming:
Including more taxa and using DGS to gather more data from fossils upsets academic results again.
Shoch et al. 2020 discuss the origin of salamanders
by directing their attention to a tiny juvenile Triassic tetrapod, Triassurus (PIN-2584/10, skull length 3.8 mm; Ivakhnenko 1978; Figs. 1–3). The discovery of a larger referred specimen (FG 596/V/20), provided Schoch et al. a reason to reexamine the type.
Science first learned about tiny Triassurus
from Ivakhnenko 1978 (here reproduced in a book, Fig. 1). Not much detail back then.

Figure 1. Illustration and description Triassurus (Ivakhnenko 1978). Little more than the outline of the skull was illustrated back then.
The Schoch et al. tracing of the tiny holotype
(Fig. 2) likewise offers few details. DGS colors (Fig. 2) provide more and different details.

Figure 2. Triassurus in situ with tracing from Schoch et al. 2020. DGS color tracing added here. See figure 3 for a reconstruction.
Pushing those DGS details around
to create a reconstruction (Fig. 3) helps one understand the anatomy of Triassurus, enough to score it.

Figure 3. The type specimen of Triassurus in situ and reconstructed.
Scoring the Middle Triassic Triassurus type
nests it with Early Permian Gerrobatrachus (Fig. 4), one node away from extant salamanders in the large reptile tree (LRT, 1690+ taxa; subset Fig. 5). So, if Triassic Triassurus is the earliest known salamander (as Schoch et al report), then Early Permian Gerobatrachus is one, too. And it is tens of millions of year older. If Gerobatrachus is not a salamander, then both are not salamanders.

Figure 4. Gerrobatrachus adult.
The LRT tree topology
is distinctly different than the cladogram published by Shoch et al. 2020 (Fig. 6).

Figure 5. Subset of the LRT focusing on basal tetrapods including Triassurus, type and referred specimen FG 596 V 20.
Unfortunately,
the cladogram employed by Schoch et al. 2020 (Fig. 6) needs more taxa. Currently it nests Proterogyrinus as the outgroup taxon. That creates problems. Relative to the LRT (Fig. 5) one branch of the Schoch et al. cladogram is inverted such that the basalmost tetrapods, Siderops and Gerrothorax, nest as highly derived terminal taxa. The other branch with caecilians, frogs and salamanders is not inverted relative to the LRT, but in the LRT caecilians do not nest with frogs and salamanders. Caecilians nest with microsaurs in the LRT.

Figure 6. Cladogram from Schoch et al. 2020 nests both specimens of Triassurus close to salamanders. Colors match colors in figure 5.
Schoch et al. 2020 reported on Triassicus,
“to reconstruct crucial steps in the evolution of the salamander body plan, sharing numerous features with ancient amphibians, the temnospondyls. These finds push back the rock record of salamanders by 60 to 74 Ma and at the same time bridge the wide anatomic gap among salamanders, frogs, and temnospondyls.”
In the LRT the salamander body plan goes back to the Early Permian, at least.
From the abstract:
“The origin of extant amphibians remains largely obscure, with only a few early Mesozoic stem taxa known, as opposed to a much better fossil record from the mid-Jurassic on.”
In the LRT the origin of extant amphibians can be traced in detail over several dozen taxa (Fig. 5) back to Cambrian chordates.

Figure 7. Cladogram from Schoch et al. 2020. They insert Eocaecilia here derived from Doleserpeton. The LRT nests Eocaecilia with microsaurs. Note how the morphology does not fit here. Where is Apteon in this cladogram?
From the abstract:
“Yet the most ancient stem-salamanders, known from mid-Jurassic rocks, shed little light on the origin of the clade.Here we report a new specimen of Triassurus sixtelae, a hitherto enigmatic tetrapod from the Middle/Late Triassic of Kyrgyzstan, which we identify as the geologically oldest stem-group salamander.”
“The new, second specimen is derived from the same beds as the holotype, the Madygen Formation of southwestern Kyrgyzstan. It reveals a range of salamander characters in this taxon, pushing back the rock record of urodeles by at least 60 to 74 Ma (Carnian–Bathonian). In addition, this stem-salamander shares plesiomorphic characters with temnospondyls, especially branchiosaurids and amphibamiforms.”

FIgure 8. The FG 596 V20 specimen that Schoch et al. referred to Triassurus does not nest with Triassurus in the LRT. See Figure 9 for reconstruction.
Speaking of that second specimen…
a reconstruction of the narrow-snouted FG 596 V20 specimen (Fig. 8) does not look like the wide-mouth type of Triassurus. In the LRT the second larger FG 596 V20 specimen nests with the CGH129 specimen of the legless microsaur, Phlegethontia (Fig. 9) far from Triassurus and other salamanders.

Figure 9. Reconstruction of the specimen referred to Triassurus, which does not nest with Triassurus in the LRT.
What Schoch et al. identified as a large horizontal quadrate (q)
in the FG 596 V20 specimenn(Fig. 8) is re-identified here as a large humerus, larger than the ones they identified. The forelimb goes into the left mouth. The left maxilla is displaced back to the occiput.

Figure 10. Phlegethontia longissima skull (CGH 129) has relatively large temporal plates, a wide flat cranium and a long pointed rostrum.
In conclusion, the tiny Triassurus type
nests close to salamanders, but closer to Early Permian Gerobatrachus (Fig. 4). The larger referred FG 596 V20 specimen with legs (Fig. 9) nests with legless Late Carboniferous Phelgethontia (Fig. 10), far from salamanders. Adding taxa and getting deeper into the details using the DGS method upsets the simpler and inaccurate Schoch et al. tracings, tree topology and conclusions.
References
Ivakhnenko M 1978. Tailed amphibians from the Triassic and Jurassic of Middle Asia. Paleontological Journal 1978(3):84-89.
Schoch RR et al. 2020. A Triassic stem-salamander from Kyrgyzstan and the origin of salamanders, Proceedings of the National Academy of Sciences. DOI: 10.1073/pnas.2001424117
https://phys.org/news/2020-05-triassurus-sixtelae-fossil-kyrgyzstan-oldest.html