Q: Is this a legal question, or a technical question?
In other words, both. The first thing to consider is the nature of one's company, and how is it incorporated legally. But we're talking about websites so there isn't much to consider. The Internet, after all, is without borders, as is global capital. You don't need to have physical offices in different countries to cater to an international clientele.
It is absolutely 100% legal for individuals and business to use services like forwarding addresses, or even "virtual offices" in other countries to build an international presence, and register country-specific domains with said addresses. Physical offices or subsidiaries can come later if necessary. Global corporations aren't born overnight.
In short, the legal part is only providing the forwarding service with your company's articles of incorporation, and seeing to the country-specific guidelines regarding taxes and/or tariffs.
Once you have a forwarding address you can legally register the domain*. I have personally done this. Because of legislation passed due to scams, the companies involved will verify the legitimacy of your business and identity before approving your application.
This is not really a webmasters question, other than to say it is both possible and legal.
*Some countries are more strict than others though, some do require proof of citizenship.