You are mixing a technical and legal problem here. On a technical point of view, you are true, the VPN machine downloads illegal material and protects your anonymity. But on a legal point of view, it is just providing you an access to internet. So they have the same rights and obligations as any other Internet Service Provider, which indeed depends on the country.
For example in Western European countries, they are supposed to keep logs of all exchanges for at least 6 months and provide them to authorities in case of legal enquiry(*). So if you use a VPN that your local legal authorities can ask for logs, you should not use it for illegal activities. Anyway you should never have any illegal activities :-)
(*) Of course, many VPN present a policy of not keeping any user statistics, so they should not be able to answer to a request from legal authorities. But in that case they could be blamed, not for downloading illegal content but for not having kept legal traces.