Updated September 30, 2016 with the addition of taxa to the LRT and new data on Protictis.
Where DO Bats Nest? The Question Returns.
A renowned (unnamed) professor interested in the origin of bats questioned my morphological nesting of bats with Ptilocercus and Nandinia (among living taxa) and Palaechthon (among fossil taxa). The professor sent me a pdf of Meredith et al. (2011), the most recent DNA tree to lump and split living mammals, as his best hypothesis on bat origins.

Figure 1. Bats and their sisters according to Meredith et al. 2011.
Mammal Diversification
Meredith et al. (2011) sought diversification patterns and times in mammals. They constructed a molecular supermatrix for mammalian families and analyzed these data with likelihood-based methods and relaxed molecular clocks. Their results came in traditionally, with Monotremata, Marsupialia and Placentalia at the base. The latter was divided into Xenartha + Afrotheria and all other placentals, which were divided into Laurasiatheria and Euarchontoglires.
DNA Results for Bats
Lots of bats were tested and they all lumped together in a single clade subdivided into three with fruit bats (Fig. 1 in orange) separating two microbat clades (in blue and green). Bats appeared as the unresolved sisters to Carnivora and Artiodactylia. Basal insectivores (not shown hre) nested as outgroup taxa to this super clade.
That’s an overly general nesting for bats that doesn’t provide much insight. On the other hand, I wasn’t surprised to see bats nesting so close to basal carnivores, like Nandinia and the vivverids, because the morphological results recovered the same relationship. I was surprised to bats nesting close to rhinos and camels. :-) Pangolins are indeed close to bats, so we agree here (Fig. 2).

Figure 2. Bat origins cladogram. Here Onychonycteris and Pteropus represent bats.
DNA Results for Flying Lemurs
The base of the Euarchontoglires (Meredith et al. 2011, not shown in Fig. 1) included tree shrews and demopterans. I wasn’t surprised to see rabbits nesting close to Tupaia, the common tree shrew, because the morphological results recovered the same relationship. I also wasn’t surprised to see Ptilocercus, the pen-tailed tree shrew, nesting close to the flying lemurs, because the morphological results recovered the same relationship. Note these taxa didn’t nest with bats in the DNA study, but they did all nest at or near their unresolved common base.

Figure 2. Known bat ancestors to scale. Click to enlarge.
Morphological Results
The Meredith et al. (2011) results do not match the morphological evidence, which derives both bats and flying lemurs from a sister to Ptilocercus, a Paleocene pro primate and Chriacus, all close to basal carnivorans like Nandinia. Nandinia is a living carnivore that sometimes drops from trees and has an omniovorous diet. Chriacus was a long-legged tree-dwelling omnivore. Phylogenetic bracketing indicates that post-cranial characters were something like Chriacus and/or Ptilocercus. Ptilocercus is a flying lemur ancestor, but shares with bats several characters including flat ribs, a high floating scapula, wide cervicals, a rotating carpus and metatarsal + phalanx ratio similarities.
The question is…
why don’t the DNA results more closely match the morphological results, and vice versa?
DNA results cannot include fossil taxa. With bats evolving prior to the Eocene (52 mya), fossil taxa are necessary in any study on bat evolution.
The DNA of modern tree shrews and bats, etc. is not the same as the DNA of Paleocene tree shrews and bats, etc.
The Meredith et al. (2011) evidence indicates that DNA results for large clades of mammals cannot resolve large clades. DNA and amino acid results do not agree with one another in the case of large reptile clades and the same is true in large mammal clades. DNA and amino acids apparently become more useful the more closely taxa are related. The resolution is very high, for instance, in human DNA, which is why it can be used in criminal investigations.
On the Other Hand
In fossil evidence you can point to a long list or suite of homologous morphologies, from tooth cusps to phalanx ratios. DNA results cannot provides these details. Morphology will always trump DNA, especially when bats nest with camels in DNA studies. DNA can only be verified with morphological evidence. DNA results can guide our efforts but the bottom line is morphology. The Meredith et al. (2011) study was unable to provide a specific sister taxon to bats. The morphological study provided Chriacus. When closer sisters are discovered, they will be reported.
Dermopterans and Bats
Flying lemurs nested close to bats and bat babys have short fingers like those of flying lemurs. Problem is: Ptilocercus, which comes between the two, has no extradermal membranes or webbed fingers and its limbs are not elongated. I have no answers for that other than both bats and flying lemurs are about 60 million years old and likely had a common long-limbed ancestor with extradermal membranes in a sister to Ptilocercus. Or bats and flying lemurs both developed extradermal membranes by convergence. Or Ptilocercus lost its ancestral long limbs and membranes.
Can we trust results?
In science we don’t trust anything. Not DNA. Not morphology. Everything is tentative and provisional.
References
Meredith RW et al. 2011. Impacts of the Cretaceous Terrestrial Revolution and KPg Extinction on Mammal Diversification. Science 334:521-524.