I don't quite follow, why would a communist society have more incentive to lie about statistics? This seems like quite a big leap. As somebody else noted, during the beginning of great leap forward, there were huge misrepresentations about crop yields and similar things -- but this was _not_ due to a one-party system per se, it was because the farmers had promised bigger yields due to the now "modern" communist methods of planting crops and similar things. Everybody bought into the idea, and when it failed to come through, nobody wanted to take blame.
I don't think that communist societies have more incentive to lie about statistics. But they have less incentive to catch lies about statistics, because there is less competition. If the government collectively manages all the means of production, then all the routes to power go through the government. If the government chooses to lie about statistics, who else has the power or opportunity to challenge it?
In a capitalist system, it's possible for private citizens to achieve financial success without going through the government, collect and publish their own information, and in doing so, challenge and influence the government.
