Stats have value, but there are other factors as well. It's not just "heart" whatever that is. It's also opportunity. For whatever reason, Josh Allen did not have the opportunity to participate in a big time high school program. That led to him not getting a real opportunity to go to a 4 year college with a chance to start. Instead, he went to a small time community college. Even that did not get him a scholarship offer from a division 1 school. He always had to settle for leftovers. A kid can react to the lack of opportunity by giving up, or he can decide he's going to outwork everybody else and prove them wrong. Fortunately, Allen had the raw talent to succeed and personality wise, he turned out to be the latter, a guy who is going to outwork and out compete everybody else, and prove them wrong.
I'm sure the Bills scouting staff crunched all the numbers, including pro day performance, but fortunately they dug deeper and talked to Josh Allen's coaches along the way. Of course, they interviewed Allen as well. So I'm going to give some credit to Brandon Beane. It's about analytics, but not just about analytics. He made a decision based on his belief that the intangibles he and the scouting staff sensed in Allen from all the extra work they did, that he was better than his stats.
It should be noted that the Bills were not the only team impressed with Allen. You may recall that the Arizona Cardinals were heavily rumored to be planning to take Josh Allen when Buffalo traded up to ***** him out from under their noses. Nobody can prove that, but it's reasonably plausible.