Impossible to select a subdocument with blank field name ( "" )

Situation: some MongoDB documents have subdocuments that contain an empty key, e.g. (I stripped ObjectIDs to make the code look nicer):

{ 

    "_id" : ObjectId("..."), 

    "stats" : 

        { 

            "violations" : 0, 

            "cost" : 170, 

        }, 

    "parameters" : 

        { 

            "" : "../instances/comp/comp20.ectt", 

            "repetition" : 29, 

            "time" : 600000 

        }, 

    "batch" : ObjectId("..."), 

    "system" : "Linux 3.5.0-27-generic", 

    "host" : "host3", 

    "date_started" : ISODate("2013-05-14T16:46:46.788Z"), 

    "date_stopped" : ISODate("2013-05-14T16:56:48.483Z"), 

    "copy" : false

}

The problem is line:

"" : "../instances/comp/comp20.ectt"

it is impossible to get back the value of the field. Querying doesn't work:

db.experiments.find(

,

)

gets the full content of the parameters subdocument. (My guess is that "." is probably ignored if followed by an empty selector.) From the JSON specification (15.12.*) it looks like empty keys are allowed.
Moreover, renaming doesn't work either, for similar reasons.