Yes. Since BYU is a private institution and this is written in the document this kid signed and agreed to abide by, they have every legal and moral right to do what they have done. Period.
Then BYU decided to refuse him the award.
It makes one wonder how long they watch you. What if it is ten years, five years, instead of one month.
Does a graduate have to walk on egg shells their entire life, looking over their shoulders wondering if this activity or that activity will mean BYU will snatch thier degree.
Private institutions still have rules to abide by due to their interaction both with licensing and finical aid. For example BYU has to abide by Title 9 polices.
Private institutions in this day and age have to give over some of their control for their degrees to mean anything and for the students to compete in the general population.
Been there done that from the institutional side.