I'm really sorry -- but do go through with the additional infusions! Indeed, sometimes these tests do come back as a "false positive", and sometimes a repeated test will have very different results.
I don't know much about Tysabri at all..but I know that for the interferons there are antibody tests, and a lot of confusion...some doctors think the "positive" results mean the patient should stop the drug, others are as convinced that it doesn't mean anything. You might ask your doctor for his thoughts about what it does mean to him, and what he'd advise...but then, maybe you already have a sense of that, as he's having you continue anyway.
I hope this all gets sorted out for you.
...I am not a doctor, nor health professional, and don't pretend to be one, here.....