I did NeedAccess because there were several schools to which I applied that required the form. Truly, it was one of the most heinous experiences of the application process. But I'm a poor and I need money so I sucked it up.
From the website, it seems as if Need Access is only for those who are noted to be eligible for grants. If it says you're ineligible, just from reading the website it would seem as if you don't need to do NA. However, since you truly believe you are needy, this is why I'm encouraging you to speak to the Financial Aid office. There may be some way you can appeal or something.