The key idea is that there is no true timestamp. This is really hard to get across in simple examples, because we almost always describe the example from an objective, external viewpoint, and then start discussing how things appear from different perspectives in the example. But the supposedly "objective" viewpoint is just a different viewpoint that we've invented, it is no more accurate than either of the other ones.

So yes, Alice, Bob, and Charlie can all calculate the timestamps relative to the other positions, and they could collectively decide together that one of those options will count as the "true" measuring point. But this is still a measurement decision that they have made.