I'll argue this.
Looking through Ortiz's hit charts for Fenway park from '06-'09 you can easily verify the fact that Papi's use of the opposite field is minimal this year, while in his best seasons ('06 and '07), a considerable number of his hits went to the opposite way beating the shift.
And we're not just talking singles, but also a lot of doubles and a couple homers per seasons.
So, in essence, his inability to use the whole field may not have affected his power numbers a lot, but it has greatly affected his batting average and ability to get on base.
http://boston.redsox.mlb.com/stats/individual_player_hitting_chart.jsp?c_id=bos&playerID=120074&statType=1