Starting with the assumption the other players on scholarship are coming back and are "on pace to graduate" then my understanding is as follows (haven't thought about APR in awhile):
Samuel and Lubin depend on two factors: 1) GPA and 2) where they transfer. If they transfer to another D1 program on scholarship with a high enough GPA UConn should be able to get a waiver to maintain a perfect score.
For Boatright, as long as he was on pace to graduate (I believe they assume in five years) and he has a high enough GPA then he should be fine regardless of if he actually graduates. So if a normal student needs 120 credits to graduate in four years, Boat would need to have 96, including on pace for all other requirements (major, general requirements, GPA, etc.)
One and dones are held to the same standard as Boatright, so they only need 24 credit hours and a high enough GPA plus normal freshmen standards. This is usually much more lenient than for upperclassmen. Transfers usually have a higher standard (GPA) than those leaving early for the NBA.
Either way, the past few years UCONN has had a very good score and it's a rolling score the school has to worry about. One bad year doesn't matter as long as the next few years are OK.