Retrieving rail tickets from Kiosk

If you paid by PayPal yes any credit card will do. I do that all the time. The card is merely to prove ID. I use any of three cards and vary it, so that certainly works.
I have no idea what a virtual card number is so can't help you there. I have never heard of such a thing.

Retailers can set the flag for any card collection but from the statement you quote that isn't the case for the one you used. You shouldn't use virtual cards for these retailers for paper ticket collection, although you can do Apple pay, Google pay, PayPal etc or other delivery mechanisms

For the one you have used the virtual card, you can try machine ticket collection with another card, and if this doesn't work go to a ticket office that should be able to do it with your reference number and some ID.

I picked up all my train tickets at the kiosk in the train station in York in July and all they needed were the confirmation numbers for each itinerary. No credit card was asked for though I did read when making the reservation that it would be required. We bought tickets on the TransPennine trains.

That sounds unusual Nadine. Normally you have to insert or tap the credit card before you can get to the screen to insert your collection number.

Sorry - I should not have said kiosks.
I went to the customer service office in the train station, not the kiosks.
I figured it would be better to have an agent print my tickets to avoid any issues.
The OP could do that and would likely not need a credit card to retrieve the tickets.

I had the opposite experience of Nadine this summer. I picked up prepaid train tickets at the ticket windows in Canterbury and Bath and both times I had to tap my credit card (for a £0 “charge”) to get the tickets.

If there is a ticket office open at the station, go and ask them for help. They are well used to sorting out problems!

Just a quick note if you don't want to go to the hassle of having to pick up tickets at a kiosk. Some rail lines will only issue mtickets, which are the ones that you have to pick up in person. I wanted to have my tickets already in hand - loaded into my Google wallet and pre-printed at home (I'm old school and don't yet completely trust digital tickets, or my phone not dying on me) - so I looked for etickets. (Thanks to a forum member who posted on another travel site when I asked about it.)

If one rail line doesn't offer etickets, you can go back a (web)page, switch train lines, and find one that does offer etickets. In my case, the first time I ordered, the rail line ScotRail offered the tickets, but only with mtickets. I went back, switched to Greater Anglia, and was able to get the etickets. All of mine are now safely in hand, waiting for our September trip.

M-tickets are ones that are stored in a specific company app (the name comes from mobile-ticket) and require activation before use. E-tickets are also can be delivered into an app but are also sent in a pdf which can be used directly or printed out, and sometimes can be put into a digital wallet such as Apple or Google. M-tickets are becoming rare fortunately.

Some journeys can't have any kind of electronic tickets; any involving TfL & Merseyrail are two examples, so any journey crossing London requires collection of a paper ticket.