She offers different theories to explain the similarities. Personally I come down on the side of Theory 2 (or Theory 3), that 'As the mosaic may itself be a copy, then maybe some other version of the original prototype did survive till the mid seventeenth century – or a version of a version of a version. The similarity in other words is a consequence of both works of art going back to the same prototype, but is not a consequence of Pietro actually having copied the mosaic.' It is true that there are no other surviving versions of the mosaic, but it seems that there were ancient paintings of the battle. Pliny the Elder mentions one by Philoxenos of Eretia in his Natural History (34.110). So the battle scene certainly existed in antiquity, and Italian scholars in particular accept that the Alexander mosaic derives from an early Hellenistic prototype (see Zevi's 1998 discussion and De Caro's 2001 booklet on the House of the Faun).
So, it's true that there is no direct evidence of a version of the battle having survived until the 17th century, but the House of the Faun mosaic was not the only depiction of this famous battle in antiquity - so maybe a version, or a memory of a version, did survive into the 17th century? I'd be interested to know what the rest of you think!