The main point of the news you're talking about is that foreigners should use border checkes during traveling between two countries, and that there are no such borders checks while traveling by car or train, because of "union" of the two states, so, even if you have sufficient documents to get back into Russia, there could be no person able to check them at the border. So, you could try to get back to Russia by plane, as there is border checks in the airports (still may be not an option, you should contact the officials for this).
Update:
Some decisions of Russian aren't understandable. More on that: there is a train from Ukraine to Russia via Belarus, and foreigners can use that because there will be a border check at the end. But if you're traveling by car, no one can guarantee you will pass border because Russia set up different rules for foreigners and Belarus residents. No-visa agreement was setup only for Belarus residents, as it appears right now, not for everybody.