Not sure how you're even reading that anything in these instances was "under the table", it was all above board with the chains of command and the CM involved.
The choices to the members were simple, be promoted and posted or decline the promotion and stay in situ. As PuckChaser pointed out, they were still liable for posting anyway if they declined the promotion simply to try to avoid a posting but the "deal" was they wouldn't be and they would be left in place for at least one more year. An "under the table deal" would have been something along the lines of promoting the member and letting them sit in a MMO position while another unit went vacant at a key command team rank, while they stayed in location without an actual job to do.
As for why they would give up a promotion they earned, it's pretty simple. They were the ones asking not to be moved to accommodate a family situation. As a reminder, every rank change instruction states, "THIS PROMOTION IS CONDITIONAL UPON THE MEMBER ACTUALLY CARRYING OUT THE ASSIGNED DUTIES AT THE HIGHER RANK AND AT SUCH PLACE WHERE THE SERVICE REQUIREMENT EXISTS". If a member is asking for special consideration and part of that makes them unable to meet that simple requirement, they shouldn't expect to be promoted.
Ref your idea about compassionate status... This makes the member ineligible for promotion so they'd have to move first in order to be promoted anyway and then try to get a compassionate posting back to that location.