All experimental evidence suggests that the transfer of information faster than the speed of light in a vacuum is impossible. Scientists understand full well that there is always a possibility some new discovery could upend even the most fundamental view of the universe, but until evidence to suggest otherwise comes along, scientists can only work with the experimental data they have -- and so far, all of that suggests FTL transfer of information is impossible.
Therefore, drawing from the incredible amount of experimental data, it is reasonable to conclude that such stars could not have conspired with phenomenon on Earth, since the information would need to have left Earth, reached the star, then returned. The universe simply isn't old enough for such a round trip to have happened. If the max speed you can travel is 1,000 miles in an hour, and the universe is one hour old, then it is impossible to make a round trip to a destination 1,000 miles away. Therefore, if someone arrives from that destination, we know it is impossible for them to have conspired with someone from where you are at, since such a round trip would have taken at least two hours, and the universe is only one hour old.