from what I understand.

Pita signed a scholarship agreement with BYU with the understanding that he was serving a mission and then after returning in 2 years, they'd try and work out the qualification issues, or have him come to school for one year as a student and get a year under his belt before playing football.

BYU DID send someone to Tonga to try and work out his coursework issues, but was unsuccessful. In the mean time, the assumption that Pita wanted to serve a mission was looking less likely. Also, BYU under Bronco had yet to go to the NCAA to request a waiver in any case, and did not plan to start (at this time).

At this point, Utah steps in and offers Pita a scholarship, stating they could get him qualified for school and immediate eligibility to play football without having to sit or retake courses. Utah succeeds in getting the waiver, but Pita is STILL a non-qualifier, just one who got the waiver which, under PAC12 rules, allows him to practice and play right away if he does not push Utah over their NQ allotment.

BYU was NOT planning on taking him as a non-qualifier. If this were true, why not offer him a scholarship right off the bat rather than signing the non-binding scholarship agreement?

Talo "freaked out' because Utah told Pita he could enroll and play right away and he did not think Utah would pursue the waiver and if they did, since BYU had tried and failed to resolve the course work issue on their own, Utah's appeal would certainly be denied. This is an example of where Utah gets the reputation among BYU fans for magically getting guys eligible/qualified.

So your assumption that BYU people thought that "the U was lying to him and he would never be able to get into Utah, but he could get into BYU" is not true. If BYU was planning on taking him as a non-qualifier, it would be to sit out a year. He was still a non-qualifier that Utah took, but the successful waiver allowed him immediate access to the football program.