One of the open problems in article level metrics is how to automate, quantify, and describe the exposure an article has had in popular science pieces in newspapers and general science magazines. Peter Binfield (PLoS) and Alexis-Michel Mugabushaka. (European Research Council) both brought this up at the NSF Workshop I attended yesterday.
I agree that this is needed. The old models of communication in science that either describe scholarly communication among scientists or popular communication with non-scientists are not enough. Lewenstein  and Paul  (among others) each describe different ways these systems are interwoven. Meyer and Schroeder  have hinted at ways to build a model of a combined system.
So here's my idea: why don't Science, Nature, PNAS, Journal of Biological Chemistry, Cell, New England Journal of Medicine, Physical Review Letters and the other biggies who give articles to journalists in advance of their publication and who require embargo of the story until publication REQUIRE the publications to hide the DOI somewhere on the html version of the story? So it wouldn't even have to be visible to the human reader, it could be hidden somewhere on the page, but somewhere that crawlers could find it. Hopefully folks could agree on some common place or tag.
This would benefit the newspapers and it would benefit the publishers and it would benefit all of the participants in the science communication system - including scientists outside of the research area and non-scientists.
These are only a few journals, but I would guess (and I could probably find research to show this), that they get a lot more press than other journals and other journals would not want to be left out so would probably add the requirement, too.
 Lewenstein, B. V. (1995). From fax to facts: Communication in the cold fusion saga. Social Studies of Science, 25 (3), 403-436. doi:10.1177/030631295025003001
 Paul, D. (2004). Spreading chaos: The role of popularizations in the diffusion of scientific ideas. Written Communication, 21 (1), 32-68. doi:10.1177/0741088303261035
 Meyer, E. T., & Schroeder, R. (2009). The world wide web of research and access to knowledge. Knowledge Management Research and Practice, 7(3), 218-233. doi:10.1057/kmrp.2009.13
Hi Christine, I am not sure what you mean. You would like the newspapers/popular mags to hide a journal article DOI before it is officially published? What is the advantage of hiding the DOI? Why not make it text searchable in normal HTML, since the news sources has to wait until publication anyway? Otherwise, if the DOI is findable before official publication of the journal article, then people might find the link to it and read it before it is "officially" published? I've hidden links before in clear single pixels at the bottom of screens, so it is definitely doable.
Oh, I wasn't clear. Ideally they should show the entire citation to the journal article clearly on the page. If they are unwilling to do that, they should at least have the DOI somewhere on the page where a computer can find it. That is, only once their article and the journal article are alive.
I know I'm odd, but suggesting perhaps the DOI should be present in a HTML publication sounds to me like suggesting a print article should have page numbers.
Could there be any conceivable argument *against* this other than "we don't feel like it"?