"The light minute has everything to do with being able to conclude are out of eachothers
lightcone. The only frame where the boxes would be opened simultaneously is the frame the
clocks were synched in."
Fred carrying the box away at less than light speed can NEVER get outside Elle's light cone. The idea that the light cone was limited to the distance light can traverse in one minute was an assumption of the thought experiment.
Agreed, Fred is in Elle's light cone in terms of their contact in their shared inertial frame during which their clock's were synchronized, however the event E of Elle opening her box with that of event F of Fred opening his box is space-like separated (i.e., the event F is outside the light cone of event E). If event F (at 1 light minute away from event E) happens at 12:02, then event F is in the light cone of event E since light can travel from box E to box F with time to spare. With event F occurring at 12:01 and being more than 1 light minute away, we would need to travel faster than the speed of light in order for event E to affect event F (assuming the waveform collapse interpretation of entangled systems).
Something caused the clocks to no longer be a rest with respect to eachother. Generally this includes one clock being accelerated. Subsequently the clocks are no longer in the same inertial frame [the inertial frame was the clocks at rest with respect to eachother]. If they were they would remain synchronized.
In terms of exact synchronization, of course you are correct (although, exact synchronization is not even possible anyway). However, I understand that this alone doesn't justify the breakdown of saying that two events aren't (approximately) synchronous since relativity would wreck havoc in our ordinary lives. However, one of the commonly understood interpretations of special relativity is to say that absolute simultaneity can breakdown. The breakdown of absolute simultaneity happens, I understand, when it is operationally impossible to establish clock synchronization. My understanding, and correct me where I'm wrong, is that within special relativity this is accomplished through operationalist means, and in cases where the acceleration was at relativistically significant velocities for astronomical distances, or the distances between events are astronomical distances such that you cannot even approximately synchronize two events in an operationalist manner (e.g., we cannot synchronize our clocks between us and a society living in the M31galaxy), and therefore you cannot say which event occurs first. That is, simultaneity can only be established if you can show that events are simultaneous, otherwise if not possible to do so within specifically the context of relativity, you cannot say two events are simultaneous. So, for example, we can be rather confident that if we synch our watches in New York, and you fly to L.A., and then an event that happens at 12:00 (EST) using my watch in New York and happens on your watch at 12:00:32 sec (EST), then we can definitely say (assuming our watches are accurate) that what happens at 12:00 on my watch happened first. This is because you and I are in still (roughly) in the same reference frame, and special relativity has no restrictions regarding the synchronization of these two events (at least when talking about timeframes greater than nanoseconds). This is because you, even though you flew to L.A., are still within my light cone and you didn't fly away at relativistic significant velocities for long distances. The same is not the case at one light minute away since we are talking astronomical distances and operationally we can no longer state which event happened first within the context of special relativity since event E and event F are space-like separated.
A signal would allow you to calculate the value of the desynch in the clocks [the thought experiment did include the distance between Fred and Elle]. They were synched when Fred left. Elle notes when she did her thing. Elle receives the signal from Fred sent when he did his thing. Elle accounts for the time the signal took to traverse the distance and then determines how much delta between when she did her thing and Fred did his thing. This is the value of the desynch.
This is an attempt to establish simultaneity through operationalist means after the fact. However, quantum probabilities are based at the time of the event and not after the event. If we were to consider quantum probabilities after the event, then Born's rule is no longer valid since we already know the probability of the event by simply measuring what event actually occurred. The important thing is not that we can somehow determine what event happened first (after the fact), or that we can know what quantum event happened after the event, the important issue is how to compute quantum probabilities before the event, and this requires Born's rule and it is based on knowledge we have before the event (and not after the event). Since special relativity gives us no way to know the simultaneity of an event before the event occurs, we have to include those 3 sets of equations as shown by Barrett. This is not necessarily true if we re-establish synchronization before opening the boxes at l light minute away, but the whole point is that we are not re-establishing the clock synchronization after moving outside each other's reference frames, and therefore the 3 possibilities must be included in the Born equations.