Yes it is true that if you are found medically, scholastically and physically qualified, they must offer you an appointment if you have a principal nomination.
Also scholastically is a better term than academically because not only do they look at your grades/gpa/sat scores, they also look at you involvement in sports, clubs and leadership positions.
Also, if you have a principal nomination, you shouldn't worry too much because chances are if your MOC designated you as the principal nominee, then they think you will do well and succeed at west point (they reviewed your transcripts and resume as part of your application and so they wouldn't make you a principal nominee if you weren't qualified in their eyes). This isn't always the case but in most instances is true.