As usual the media hears the churchbell ring, but doesn't know where the clapper hangs, as we would say in Dutch.
The judge didn't reject the plea deal because of the stipulation that Travis McMichael could serve his time in federal prison. The main issue actually seems to be the fact that she would be bound by the 360 months:
Federal judge rejects plea agreement in hate crime case for man who killed Ahmaud Arbery
So the issue here is the sentence duration, not the fact that Travic McMichael would serve his sentence in federal prison.
It's important to emphasize that the question where Travis McMichael serves his sentence is a matter entirely outside the purview of the judge. In this case the state has primary jurisdiction over the defendant, and the federal sentencing judge can not order the delivery of the defendant for service of sentence in a federal institution.
Mutatis mutandis, if the State DOC agrees to hand over primary jurisdiction to the Federal Bureau of Prisons, I do not see on what grounds the judge could block such a transfer. It's a matter of executive jurisdiction and entirely up to the State DOC and the Federal Bureau of Prisons.
The judge rejected the deal for two reasons. She said she wanted discretion over sentence length AND she believed the family should be allowed to express their wishes at sentencing, which the deal disallowed.
You're correct that the family's preference about where the 3 serve their sentences isn't binding. I'm thinking it's possible the judge was responding to what seems to have been a communications break down, wherever that occured, and she was trying to ensure the family's wishes were heard on the record.
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BTW & FWIW, pretty much every legal analyst/attorney I've read or listened to about what happened was appalled the judge rejected the deal. Reasons included:
1. Victim families should not be permitted to dictate sentencing or plea terms. (And by law, aren't).
2. The deal *did* serve the cause of justice, in that the MMs admitted their crimes were motivated by racial hatred. Since the purpose of a federal trial was to achieve that specific outcome, justice was achieved. And it was achieved without expending the money, time, and resources (human & otherwise) of a complex trial.
3. Some commentators were especially critical of the reason the AA family explicitly cited for rejecting the plea- their insistence the 2 spend their time in state, not federal prison.
As one said (one of my favorite attys on Twitter): he understands why the family wishes the absolute worst & most miserable conditions for AA's murderers. But. Bringing the federal charges was essentially intended as plan B, should the 3 escape justice at the State level. (The family was part of a very loud chorus insisting upon those federal charges, IIRC). That it's "freakish" to bring federal charges as insurance but to demand state incarceration if the fed charges stick.
4. The moral component. That it's telling how many *know* how bad state prison conditions are & demand that the 3 are subjected to them. That it may be satisfying to imagine these 3 being subjected to those conditions, but in reality, the majority of peeps confined in h'ellhole state prisons are the poor/ POC, the majority of peeps confined.
I especially agree about that last count. And feel genuinely chastened.