Yep, well, it wouldn't be HARD if you could just ride on the coattails of your teammate's success.
Gotta be a star player! Yeah! 
And as far as I know, the differences between Hard/Normal/Nightmare AI is simply that they gain XP and gold at different rates. If I remember correctly, Normal AI is the base, Hard AI gain +15% gold and XP, and Nightmare gains +30%. I strongly suspect that your Singleplayer-Tournament teammates are always set to Normal AI, hence their dismal long-term performance when they are pitted against Hard opponents.