I agree in general, agnosticism doesn't have to be "fence-sitting". However, I'm sure a lot of people believe that they have a connection with God.
Take schizophrenics, for example. Schizophrenics with God delusions (1/4 of schizophrenics, I think) really believe that they are either speaking to a divine being, or that they are either a reincarnation or a manifestation of said divine being.
As for more typical people, there is a tendency to attribute events to the supernatural. Ramachandran has studied this and it's very much worth watching:
http://www.youtube.com/watch?v=qIiIsDIkDtg
http://www.youtube.com/watch?v=5z4B5BYbjf8
One neuroscientist suffered damage to the left brain, through a stroke, and has shared her experience with others at a TED conference.
Drug users sometimes experience similar phenomena, presumably by affecting the brain in analogous ways.
Near-death experiences can be explained similarly.
So I don't find it unusual that normal people can find themselves in similar situations without extremely unusual neurotransmitter levels, or slightly unusual neuronal pathways.
I would say that these experiences are "real" and these people will consider themselves theists or religious, without being dishonest in the least.
As for myself, I consider myself agnostic, but with a materialist and atheist slant. That's definitely not fence-sitting, but I still contend that most people do not know for sure.