Language Log has opened up some discussion of the Ewa Dabrowska research reported below and provided links to more detail about her findings. Here's the review article and here are the Language Log links from one of their most recent posts on the topic.
A couple of interesting points come out of the readers' comments too. Two of the sets of questions in Dabrowska's research are characterised as "Q-is" or "Q-has", for example "Every umbrella is in a stand" and "Every bowl has food in it" where the respondents are presented with pictures and asked to match the statement and the image. But, as Adouma points out (in th comments to this post), one of the reasons why people taking the test may get questions like this wrong is because they're expressions that are rarely heard. In fact, Mark Liberman, the Language Log writer, suggests that in a corpus of 400 million words the pattern "Every noun is in a/an noun" never occurs. How are respondents supposed to get these right when they're "unnatural" examples of grammar?
This doesn't only raise questions about Dabrowska's research itself, but a wider issue for those of us teaching grammar. If the examples we use to illustrate grammatical concepts are not rooted in reality and genuine usage, what use are they? We could spend all day teaching examples like "Every cat is sitting in a bed" but we'd have to realise that noone would ever say or write such an expression again in their life.
edited to add: there's some Radio 4 discussion of this topic on Material World which will be available on i-player until later this week.