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.
There is no need too look at data. It's common sense. Whatever the checkout procedure is there doesn't have to be every payment option displayed at once.
The checkout procedure for one option (say a check for USD in mail) can look the exact same as a checkout procedure for multiple options, with one difference being a link or similar which says "other payment options". Now, if you're telling me you'll lose sales because of the presence of that link, then you've surprised the hell out of me.
(Note I'm not talking about heavily psychology based products like "work-at-home-and-get-rich-if-ordered-now!" landing pages where every word said makes a difference.)