The women who are accepted are (usually) verified, i.e.
their Ids get scanned and copied into the agency’s database.
There is also a gender imbalance in Russia and the Ukraine, with more women than men, which makes it both difficult to find a husband and more likely that the husband one does find will be entitled, lazy and generally unpleasant.
Western men are still seen as likely to be rich and easy to please.
Whether or not that is the woman’s choice is for you to decide. Petersburg, and also in the Ukraine, the economic situation is not great.
Many people live below the poverty line, jobs are scarce, it’s expensive to move to the big cities, and yes, one of the easiest ways to “get out” is to get married to a citizen of a Western country.
The only websites that seem to provide “real” Russian women for interested English-speaking men are essentially dating sites.