I'll sum this up very easily. First, there is no such this as tampering with coordinators. A rule was set in place a few years ago saying after the season, teams are free to interview whomever they want in this aspect.
Next, a coordinator cannot make a lateral change in teams unless both teams agree. NFL contracts restrict that from happening due to poaching and the fact $$$ could move coaches with no restrictions. A coordinator IS allowed to break a contract with an upwards shift in teams, meaning the only position Fangio could voluntarily leave the Dolphins for would be an Assistant HC / DC for another team or HC. That's it.
The other way is for the Dolphins to fire him. Tear up his contract and kick him out of the building. No matter how they phrase that "mutual" or whatever, he was fired.
Playing hardball? Most likely PHI would have or is offering him an Assistant HC position for when Sirrianni fails this year and there is f*ck all Miami could do about that.