They don't claim to be democratic, only more democratic. The alternatives compared against aren't democratic either, so the hypothetical possibility of the CCP being, on the spectrum, more democratic is theoretically sound. Reality isn't, though. The trouble with the claim is that what makes something more or less democratic in the real world is completely nebulous, allowing anyone to pick arbitrary criteria to make the claim.
> You need to know at least what side you're speaking for
Information can be inaccurate, but it doesn't have a side, fundamentally.