I wanted this too but apparently there's no diffrerence with local play. I'm told if you go online then other people cant even use tools unless you add them as best friends, but when I've played locally people can come in and chop down all my trees and dig holes or fish whatever.
So I guess they don't give you the app until you connect via internet because local play assumes you are already "best friends" with the people you are physically in the room with at the time (and if they're a dick on your island you can just throw a shoe at them irl or something).
I could be wrong but that's what I gather, also I enabled the flag for it in my game but it reset and didn't show up anyway so it's probably a server side check or something.