I don't think the main point is what flavor of card it was. It is that Amex (allegedly) repeatedly flagged, then subsequently reviewed and approved the transfers of funds from Koss corporate accounts to pay for items of an obviously personal nature on Sachdeva's account -- jewels, furs, shoes etc. (Bolding mine.)
In other words, Amex's systems worked, but were overruled from within. It would be interesting to hear exactly how Sachdeva convinced the Amex personnel that her spree was corporate-sanctioned, but I suspect we never will.