Robert_Charlton - 8:36 pm on Sep 26, 2013 (gmt 0)
You might take a look at this discussion, from a few weeks ago....
Inner page instead of home page now showing in Google search results
The topic comes up frequently, and I've seen the issue happen most often with exact match domains. In the above-referenced thread, I was thinking there might have been an inbound link anchor text issue. It may be Google's way of questioning or testing the links in some way. Or... it could be (and this is a guess meant to be a little bit ironic) that Google is giving EMDs a reverse honeymoon as a way of neutralizing their anchor text advantage.
Throwing more links at the page is probably not the right thing to do. As netmeg suggests, work on other traffic channels.
Another thought... I've seen Google return things like privacy pages when it's in a testing mode. If you have an EMD and that vocabulary is featured enough on your privacy page, "keyword cannibalization" might cause Google to check those pages. See CainIV's comments and our exchange about it in this thread...
Why Do Some Homepages Get Buried?