confused by Bell

According to Bell the following generalised statement applies:

"No physical theory of local hidden variables can ever reproduce all of the predictions of quantum theory."

If this is the case for any one theory then that theory is flawed and should should not be considered as a theory at all.

If there can ever be such a thing as a real theory of local hidden variables then it will reproduce all of the predictions of QM and it will predict what can be observed. The problem is that the details of such a theory are not yet known and nor are the details and subtleties of any detection methods known.

 How then can Bell and his followers make generalised statements about all theories without a detailed knowledge of those theories?