Is there an official visa position on the monaco payments card project? In what way is distribution of payment cards? 
No, they don't have any right to use Visa in their product. If Visa want to do something like that they can create their own crypto currency. They don't need Monaco or other projects in crypto debit card industry.
It's not about "right to use Visa in their product". VISA has to first approve their final card design before they can show any marketing material with the VISA logo. It would appear they are indeed collaborating with VISA to put out the (SWIFT) payment card.
This does not answer the question....
This coin has nothing to do with Visa. They can't use any Visa name or logo because of trademark issues. They used Visa in the past to marketing but when they realized there's a lawsuit coming they immediately remove anything related to Visa in their campaign. I don't think they can press a card that is accepted in ATM's anyway.
That was TokenCard, not us. We never had any VISA trademark on our mockups, as that's direct guideline from visa: until the final card design is approved, it should not show up in any marketing materials.
Monaco Card will allow for ATM withdrawals.