Wi-Fi and cellular systems are two completely different things. Sure, you can get some Internet service via cellular providers, but you're not always going to have the same bandwidth as you do with a true broadband Wi-Fi wireless access point (WAP), cable or DSL. (Keep in mind that Wi-Fi service like you have at airports, libraries, Internet cafes, etc. usually involves a landline broadband cable or DSL connection or a broadband sattelite link.) At best, you might have the equivalent of a 56K dial-up modem or better, but that depends on whether the cell towers where you are have been upgraded and how many are in your particular area; even here in Albuquerque, cellular-based Internet access tends to be slow and spotty in many locations, and I know it's even worse (or nonexistent) in rural areas. Amtrak might eventually provide broadband Wi-Fi service on its long-distance trains, but that would require either substantial upgrades to the cell towers along those routes (and more of them) or a satellite link (which isn't necessarily cheap and would have to be provided for each car, since a single receiver/transceiver wouldn't be adequate).

The payment system Amtrak uses probably is based on cellular technology (it's likely the same system used by the New Mexico RailRunner, which is wireless as well), but it doesn't have the same bandwidth requirements as required for internet access, so it can operate using existing cell towers. It's also quite possible (and I would say more likely) that Amtrak is using the freight railroad's own radio networks, which are quite capable of carrying low-bandwidth digital data and relaying it via modem to a remote computer.