Over-Over (pronated) grip is my choice, it works your grip more than Over-Under (pronated-supinated) IMO. The over-under has a twisting component in it that helps your grip.
The person is probably talking about a bicep injury. With the over-under I've read there may be a chance to injure your bicep (on supinated arm), but I don't know how much weight that fact carries. Straps definitely do not prevent injury unless your grip fails and you drop the weight on your toe
You shouldn't have a mixed grip for rows anyway...