Just by checking an IP address against a database, websites can usually tell if a request is coming from a VPN, a datacenter, or a residential connection. If it's not coming from a typical residential provider like Comcast or T-Mobile, but instead from something like an Amazon datacenter, it already looks suspicious - whether you're using a proxy or a VPN, and whether it's a dedicated IP or not.
On top of that, sites can also use techniques like browser fingerprinting and behavior analysis to catch people trying to spoof their identity.
In the case of MoneyGram, I think using a VPN or proxy might actually make things worse. It’s probably better to look like an American tourist visiting Argentina and needing to access their money, rather than someone in Argentina trying to impersonate an American.