<<Disclaimer:  Verify this information before applying it to your situation.>>

These descrepancies are of two, types
1. Blood test positive - biopsy negative: the antibody tests could be
false positive ( some times happens especially with gliadin IgG ) , the
antibody test may reflect a latent gluten sensitivty that ha s not done
any damage ( by definition this individual should have no symptoms), or
the biopsy is wrong because of too small a sample , just one taken , or
an error in interpretation due to lack of awareness on the part of the
pathologist of subtle changes of celiac disease ( marsh MN ,
gastroenterology, feb 1992.  )

2. Blood test negative and biopsy positive:  the blood test might have
preformed incorrectly or if gliadin alone is used it does not pick up all
celiacs. The blood test may also go negative if gluten has been reduced
in the diet before it is drawn.  If the patient is IgA deficient it
will often be negative.  The other possibility is that it is not celiac
disease on the biopsy there are some other things that can mimic celiac
disease on biopsy.
All in all no tests are perfect
Joe Murray