In addition to the other comments, I believe it would be harder for even the present-day Russian government to go backwards and acknowledge that the other flights happened.
In fact, it is logical to assume other flights did happen. In-flight testing has long been a feature of achievement in all aspects of science. Plus, the then Soviet government would have been looking to have an edge on NASA by being able to say, "look, we have already put a man in space." But, they would have needed to be in control and that means the landing would have needed to be precise. The reason, I think, that Gagarin's flight was admitted to in mid-flight may have been because the US had picked it up on their scans.
NASA took the more cautious approach by thoroughly testing everything on the ground before sending a manned flight into space.