Absolutely, totally, emphatically disagree. I think there is no question that Battier was the best player on the 2001 team.
Oh, it was close offensively and if that was the total measure, then Williams might have had a slight edge -- his 21.6 ppg were slightly better than Battier's 19.9 ppg.
Their shooting percentage were very similar, except from the FT line, where Battier was MUCH better (79.6 to 65.9). Williams did have a lot more more assists, but Battier had a lot more rebounds -- reflecting the different roles they played.
So offensively, I'd be willing to give Williams a slight, slight edge in 2001.
But any Duke fan should know that offense is not the entire game. Battier was the best defensive player in the nation in 2001 and one of the 2 or 3 best defenders in modern basketball history. Williams was not a bad defender, but he did not even make the ACC coaches' All-ACC Defensive Team. Battier was the NABC National Defensive Player of the Year,.
He was also the consensus National Player of the Year overall, winning every major award, except the NABC Award (which went to Williams).
Battier was clearly the leader of the 2001 team (co-captain, along with Nate). He was the key player in the key games -- the reason he was the Final Four MVP. He also won the Case Award that season as the ACC Tournament MVP. In an inexplicable vote, he shared the ACC Player of the Year Award with UNC's Joe Forte (but ahead of Williams).
So, I agree that it's not up for debate -- Shane Battier was the best player on the 2001 team.