I think you may wrong.

Since his friend is working for a non-profit orgorganization, her H-1B is not under quota, so it definitely can start at any time. I don't know if her filing contains some wrong info, for example, her employer wrongly filed her staring date as Oct 1st, instead of Aug 1st, which she can.

However, I really don't know what to do now. Maybe she can contact INS through her employer, trying to fix the problem.

Good luck to her!