One might think of simultaneity as a bond between certain events. If two events in K happen at the same coordinate time, they are connected by "now".
However, two events that happen at different times in K can also be connected by "now", provided there exists another inertial frame relative to which the very same two events happen simultaneously. Moreover, assuming that the bond is transitive, it can be shown that in fact any two events are connected this way, i.e. all the events of the world (ever) are simultaneous. Yet at our outset, non-simultaneous events did seem to exist.
Instead of spending a lot of time figuring out what this really means, we rather throw out this elusive, action-at-a-distance-flavor bond and interpret inertial frame wide simultaneity as a mere definition without any immediate physical content.