Rossby, You are right, it is a form of arbitrage.

Rebates on credit cards are more like coupons then arbitrage.  Just about everyone who is responsible with their finances has credit cards with some cash payback or free airline tickets.  But, not many of those same people would take it to another level as I do.

Eventhough we see it as throwing money away, your Sister's way of financing gives her peace of mind.