A new paper in PLoS criticizes this view suggesting that there is very little evidence in support of it, and offers an interesting alternative interpretation of Azhdarchid morphology.
From the abstract of the paper:
Azhdarchids lack the many cranial specialisations exhibited by extant skim-feeding birds, most notably the laterally compressed lower jaw and shock absorbing apparatus required for this feeding style. … Taphonomic data indicates that azhdarchids predominately inhabited inland settings … We argue that azhdarchids were stork- or ground hornbill-like generalists, foraging in diverse environments for small animals and carrion. Proficient terrestrial abilities and a relatively inflexible neck are in agreement with this interpretation.
Reconstructed skeleton of Zhejiangopterus linhaiensis based on  and . Scale bar represents 500 mm.
The method used to draw these conclusions included comparison of azhdarchid morphology with the morphology of living animals. For instance, wading birds have weight-spreading feet. If azhdarchids waded, they should too. Skim feeders should have robust jaw joints (to handle repeatedly impacting the water with the lower jaw while flying along). Azhdarchids should as well. While it is possible that azhdarchids have adaptations that are not represented in living systems, exclusion of likely adaptations or suggestions of possible adaptations from living morphology is a more solid way to make inferences than guessing about what we can’t see or know.
Here is a quick summary of the various adaptations considered, and the verdict (from this paper) for each one.
Scavenging. It has been suggested that various species of achdarchid were scavenger, even obligate scavengers. In my view, scavenging is not only the last resort for many predators as a way of getting food, it is also a last resort for many palaeontologists trying to explain ancient adaptations. In any event, the present paper suggests that obligate scavenging was unlikely because of the lack of the typical adaptations found in such animals.
Probing. It has been suggested “that azhdarchids may have probed
into sediments in search of infaunal invertebrates.” However, cranial adaptations found in such living forms are not seen, so this is unlikely.
Mid-air predation (of smaller flying animals) has been suggested. Unlike living mid-air predators (such as falcons) these flying reptiles would need to use their jaws rather than claws to grab prey. However, the head and jaws are not well adapted for this.
Swimming and diving, like loons I suppose, has been suggested but there is really no evidence supporting this from the morphology.
Skim feeding is, as noted above, one of the favorite adaptations attributed to azhdarchids.
However, the hypothesis that azhdarchids may have been skimfeeders fails to acknowledge the remarkable and highly distinctive specialisations necessary for skim-feeding and ignores the fact that, among extant vertebrates, habitual skimming is unique to Rynchops … although Royal terns Thalasseus maximus and Caspian terns Hydroprogne caspia are known to perform facultative skimfeeding behaviour … The head and neck of Rynchops has 30 skimming adaptations … No azhdarchid exhibits any of these adaptations nor any
functional alternatives, and in many details azhdarchids appear
maladapted for skim-feeding….
Yet another beautiful hypothesis moidered by a band of ugly facts! But wait, there’s more!
DipFeeding and Wading. “Many elements of the azhdarchid skeleton that preclude skim-feeding also apply to their inability to dip-feed (our use of the term dip-feeding here applies to the style of foraging practised by frigatebirds, gulls and terns where prey items at or near the water surface are picked up by the bird while it is on the wing).” … As for wading, there is some agreement in the anatomy but there is a lack of the expected adaptations in the feet.
So, let’s see, looking over this paper, we seem to have run out of idea. Oh wait, no, there is ONE more idea left. Expect this to be a good one, as in most papers of this sort, the idea the authors like best is left for last. And the idea is …
Terrestrial stalking… Our interpretation of the evidence has led us to conclude that azhdarchids severed the ties with aquatic foraging conventionally assumed for pterosaurs … and that they were instead terrestrial opportunists, finding much of their food via terrestrial, ground-level foraging.
Studies of pterosaur ecology have suffered from the dogmatic attitude that pterosaurs were predominately aerial piscivores living in coastal settings, in spite of steady accretion of evidence that they occupied a variety of ecological roles in a suite of environments. The unusual anatomy of azhdarchids strongly indicates that they had a unique ecology and inhabited unusual environments compared to many other pterosaurs: these details have been overlooked by most authors who have interpreted azhdarchids as marine piscivores occupying niches conventionally considered typical of pterosaurs as a whole. This unusual lifestyle may explain the resilience of azhdarchids to decline in contrast to other Cretaceous pterosaur lineages, few or none of which persisted to the late Maastrichtian as did azhdarchids. It is hoped that this rerevaluation of azhdarchid ecology will inspire much-needed descriptions of azhdarchid material, empirical testing of the hypotheses presented here, and further research into the lifestyles of pterosaurs beyond their flight capability.
And this is what it looked like:
Life restoration of a group of giant azhdarchids, Quetzalcoatlus northropi, foraging on a Cretaceous fern prairie. A juvenile titanosaur has been procured by one pterosaur, while the others stalk through the scrub in search of small vertebrates and other foodstuffs.
For more information on this research, you should see Darren Naish’s blog post: Terrestrial stalking azhdarchids, the paper Also, Afarensis now has a post on this paper: Azhdarchid Fossil Distribution and Taphonomy