Yes, blood work can be falsely positive, as can any test in medicine, especially at low titers. However, it may be that the biopsy was done or read incorrectly or that there’s not yet enough damage in the small intestine to diagnose celiac disease. A second opinion at a celiac center can help clarify a diagnosis. False positives vary between the tests and also between the populations considered. For instance, tTG is falsely positive in about 2-3% of people in general, but in about 20% of those with Type 1 Diabetes or other autoimmune conditions.