Point #2 is patently false. Yes, it sounds counter-intuitive because it's not true. Giving the customer more payment options always increases sales, because it expands who can be a customer. If some product is desired at all then having maximum options to pay for it is a bonus/benefit, not a drawback.
Do you know that because you've actually looked at data and measured it or are you just assuming, because the person you're quoting likely has.