Mangini wanted to leave to be a head coach so that is not the same thing the only way that would be a good point would be if Mangini wanted to go to be the jets as, dc & assistent to head coach & ne blocked that
But the point is that assistant head coach means nothing in terms of level in the heirarchy right now.
You cannot leave a job as a coordinator for another job as a coordinator even if they add assistant head coach to the title.
Technically you cannot leave a job as any of the primary assistants (OC, DC, QB, ST, OA, QC) for a job as any of the others, although in practice it is very hard to turn down a step up to a coordinator position for one of your people because that will effect how other prospective coaches look at you.
I believe the restriction does not apply to contracts signed prior to the NFL Management Council decision that was made to coincide with the new CBA.
The reason the change was made was that Dan Snyder was driving the price of assistants throught the roof and the NFL decided to step in and stop that. It also resolved a lingering question relating back to ways the Bill Parcells operated at New England and the Jets, when he liberally sprinkled around extra special sounding titles to try to tie people to the team.