Two factoids of interest:

1. André was the older brother of philosopher Simone Weil.

2. "Weil" is a jumbled version of "Levi" adopted by some so as to be less conspicuously Jewish, and thus be less likely to be persecuted or discriminated against.

I wonder if this is a hint to a more-specific rumor. Weil constructed what are now known as "abelian varieties of Weil type". In low dimensions the Hodge conjecture has been proven for abelian varieties of Weil type, but it's open in higher dimensions. Maybe that's where they found their counterexample.