I was thinking all private trades can count for the weekly charts/overall charts. The only difference between private and public trades is that private, allows players sell something to another player without worrying that someone else will buy it, so why not have the private trades count?

Private trades won't be included into ratings because it's very easy to bump up the rating without actually selling anything. Player makes an agreement with another player or simply makes a second account, and sending the same pet for 10k 100 times from one account to another. Both accounts get +1000k for ratings without actually trading. Of course, this can be done through auctions too but such machinations will be visible for all players and most likely will be noticed and reported, while private trades are fully private and aren't visible to the public.