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I was thinking something along those lines, when you said private networks, do you mean VPNs? I also thought they might just be connected to a local server at the station itself, and that server is connected to the internet (on a private network).
Ticket machines generally aren't on the internet but use private networks. The payment terminal often is (nowadays) but these must be isolated due to PCI/DSS with only a limited serial / USB connection for control flow.
like so:
[ vending machine ] --lan-- [ station control ] --wan or VPN-- [ backoffice ] | | (control only) | [ terminal ] ---- [internet or local network payment gateway]