Exactly. There’s a difference between need blind and need ignorant. There are plenty of “tells” throughout an application that can point pretty firmly in one direction or the other as to whether the person likely applied for FA, even if not definitive.
Schools can and do solicit and accept donations that are specifically earmarked for FA. You can often too get even more specific (e.g. FA for FGLI, FA for a kid from my hometown, my HS, etc.) And of course as @blossom mentioned, there are also ‘unrestricted’ or ‘undirected’ funds given.