I think maybe I understand why Dr. Fine is not publishing. He has a little data on his website showing that he has sacrificed specificity in order to have high sensitivity on his tests, and he pretty much says as much in the accompanying test. I'm not sure the way he has defined the reference ranges would survive a peer review.
Skylarks's point is a good one. If by "reliable" you mean "truthful", no test will be reliable. Even serologic tests for celiac have what I consider to be a high false negative rate (report negative results when subject has celiac). However, if by "reliable" you mean "helpful in decisionmaking", I consider the test reliable.
I don't believe my Enterolab test was dead on truthful, but it aided me in deciding to give up gluten. Other factors that aided the decision included family history, children diagnosed by biopsy, the subsequent dietary response, and response when gluten is unexpectedly reintroduced (i.e. "glutened").
Untimately, the preponderance of evidence is what counted for me. For someone who is a silent celiac, however, the answer may be different.