I don’t have a smartphone and need to get my ticket from the kiosk at the Amtrak station. The kiosk requires a credit card, but my company charges tickets to a central credit card. How does this work?

Yes, the kiosk requires a credit card, but it’s only for identification. It reads your name from the magnetic strip. That’s it. So you only need a card in your own name, but it doesn’t need to be the card that was used to pay for the ticket.