Does lack of plausible alternatives for a given hypothesis count as non-empirical evidence for that hypothesis?

In the recent excitement on the discovery of the Higgs boson, and the accompanying relief that the standard model, at least for moment, holds, I had to think about a paper by Dawid, Hartmann and Sprenger, published online earlier this year. They examine whether or not a lack of plausible alternative explanations to a given scientific hypothesis - in spite of our best efforts to come up with them - could be a form of non-empirical evidence. They argue that scientists often make arguments of this kind "despite our best efforts, the only hypothesis to reasonably explain E is H. This very fact counts as evidence to support H". This they dub "the no alternatives argument" (NAA).

Thomas Kelly wrote in his lovely essay on belief polarization that our assessment of a given hypothesis H in the light of evidence E, our assessment of H does not only depend on E, and not even only on E in conjunction with other background knowledge. But it "crucially depends on the presence or absence of competitors in the field". The standard example, the demise of the design hypothesis in the light of Darwinian evolution, is provided to clarify this. Prior to Darwin, the design hypothesis H_d explained apparent design in nature (E) well and was in line with other beliefs about God's nature and existence (B). However, the evolutionary hypothesis H_e proposed by Darwin and Wallace delivered a serious blow to H_d, because there was now a plausible alternative hypothesis of apparent design in nature. (There were pre-darwinian naturalistic alternatives, like Epicurean chance hypothesis, but these were not very compelling, unless one accorded a very low prior probability to the existence of God/the gods).

On the face of it, NAA sounds like a bad form of reasoning. Argument from ignorance, or worse, argument from incompetence come to mind. And it seems to fly in the face of historical examples, and our intuitions about unconceived alternative theories. Yet, Dawid et al. go on to provide a Bayesian analysis that plausibly shows that under a variety of conditions, despite the underdetermination of theories by data, the fact that some H is the only plausible candidate to explain E counts as significant, but defeasible evidence for H (you can read the paper for details and a formal proof). 

The Higgs model, although not an independent theory, is a good illustration of the NAA. Dawid ea. propose (in an earlier version of their paper, here) that trust in the Higgs model is based on the NAA: "Scientists believe that no convincing alternative field theoretical account of mass generation exists. They believe that there is no adequate description of the phenomenology of the Standard Model that does not look like a field theory at the relevant energy scales." Similarly, cosmic inflation is felt by astrophysicists as extremely plausible in part by virtue of the fact that there are no serious alternatives (steady state ea. don't explain all the evidence that cosmic inflation explains).