Well, it’s more important to understand how/if the college defines first gen. At least for the Common Application, there is no box to check on the app that asks, “Are you first generation?” The applicant would simply list the parent(s)’ education, and each college will use that info as it sees fit (if at all). Also, at least for the Common App, any questions regarding grandparents would be on the school-specific part, and generally are only asked in connection with whether the grandparents attended that university.
Similarly, there is no box that asks “Are you legacy?” or “Are you an underrepresented minority?” The college will glean that info from elsewhere in the app and again, use it or not use it as it so chooses.
But for me personally, my definition would match, as an example, Brown’s.
https://www.brown.edu/campus-life/support/first-generation-students/faq-0
Although other colleges may use different definitions, (e.g. attending college vs. graduating).
As an example of a different definition, Harvard says:
https://college.harvard.edu/admissions/hear-our-students/first-generation-students
where Harvard includes grandparents and “immediate family” at least from an HR perspective, if not expressly from an admissions perspective.
https://hr.harvard.edu/staff-personnel-manual/time-away-work/other-paid-absences
Let’s not use euphemisms - this is lying, which could have a negative impact on the applicant if the application is rejected or the admission is rescinded.
Anyway, I can personally add nothing further for your story, as I am not first-gen, regardless of how one defines it.
On another note, putting on my moderator’s hat, the user does have permission to post this question.