Gonna have to disagree with this as well unless he is under a current offer letter.
If your scenario is true, if he turns down "the offer" he has willingly resigned.
They don't have to offer him an offer letter.
They are required to give him a new offer letter when there is a significant change in his work schedule (change of shift, changing to/from a schedule that does/doesn't require work on weekends). He went from a schedule that required work on Sundays to one that didn't any weekend work and the change wasn't made with an offer letter, though it should have been.
Now they are wanting him to go back to a schedule that requires weekend work. Since he was never given a letter when his schedule was changed to no weekend work, his position is still classified as one that works during the weekend and they can switch which weekend day he works nearly at will.
Had he been presented with (and signed) an offer letter when he moved to M-friend, he could turn down this most recent change in lieu of other options.