I disagree to an extent. I definitely agree that the girl should come to see the man and live for a time before the marriage if at all possible. But that still does not preclude the man from visiting first and it is a useful visit. The important thing in a relationship is not speed, but finding the right person.
Here's an example from my last girlfriend (and only serious relationship since my divorce): we met on this site, communicated, became close. I then visited her in Kharkov. It was a chance to meet her in her own environment, which I want to see. I want to meet her friends, see how she lives, meet her family.
Then she (and her sister) visited briefly a few months later. They flew in to Las Vegas and we also saw LA. This was still just like a vacation, but gave her a chance to see the city and a brief view of the life, as they stayed in my home. Later that year, she came again for 2 months and while we found that she did not want to live here, better to learn now and not after the marriage. This process takes more time, but less chance of a failure.
And of course, there is a difference in a Russian girl going to Europe, which is much easier to get a visa than coming to the US.