You seem to have the correct interpretation of Princeton's policies.
Most schools do not require that both divorced parents fill out financial aid forms. For schools that only require FAFSA, only the custodial parent fills out the form and the non-custodial parent's income and assets are not reported. For schools that require the CSS Profile, the majority do not require the non-custodial parent to report income or assets.
https://profileonline.collegeboard.c...ionServlet.srv
Others will point out that the top schools such as Princeton have their own forms and policies for non-custodial reporting, which is true, but these are not "most schools".