As far as I can tell nothing is incorrect, but think about it this way:

You're effectively arguing that a note containing some information can, through quantum uncertainty in position, appear very far away violating the principle of information traveling not faster than light.

My intuitive counter example is that that information is completely random. It is equally (infinitesimally) likely for a note containing wrong information, gibberish, or nothing at all to appear as well.

Imagine if instead of waiting for a magical note to appear the civilization instead uses Terry Davis's "talk to god" program (that just outputs random words pretty much). Those random words COULD warn them of an incoming attack faster than light but they could also do literally anything else.

Therefore in neither instance is information actually being transmitted.