That's certainly possible, but by no means a given. By that logic, most of God's chosen leaders and prophets throughout history would be disqualified. Moses was a murderer; David sent an underling to his death so he could sleep with the man's wife; Jacob, the man whom the nation of Israel was named for, was called "the deceiver" because he tricked his brother out of the latter's birthright; Solomon, whom the Bible states was the wisest man who ever lived, married pagan women; Paul arrested Christians and helped send them to their deaths; etc. Unless you would argue that what Hugh Freeze did is worse than murder, or adultery, or stealing a sibling's inheritance, or sending innocent people to their deaths, it's hard to make the argument that Liberty acted foolishly. It's much easier to argue that they lived out their Christian faith in this situation.
Well you certainly get an A for biblical history, however Freeze has demonstrated the behavior of a confidence man in his past, and confidence men are notorious for taking advantage of sentimentality and making people feel like they are doing good deeds by helping them. People who are responsible for others, especially young people don't have the freedom to indulge their conscience, they have to be good stewards and try to exercise good judgment in separating the wheat from the chaff.
In any event, I don't think your bibical examples are really very analogous or guiding in this situation, God forgave these people sure, but God's judgment is perfect, he sees people's hearts. We don't, we can only discern as best we can from the facts available. For every authentic repentance that occurs in the Bible or in real life, there are many that are not authentic. This isn't a matter of deciding whether Hugh Freeze should live or be a free man, this is a matter of deciding whether, 16 odd months after he put a lot of young men's future into great uncertainty, hurt his family and many other people, lied to authorities, and whored around on his wife, if he should be given stewardship over another 100 or so other young men and hundreds of thousands of dollars. And I stand by my opinion that I don't think Liberty has made the wisest choice in this matter.
As for 3 of your 5 biblical examples (David, Solomon, and Jacob) their authority was hereditary, they never lost it and no one had to discern whether to give it back to them, so they aren't really very helpful. David was king when his issue occurred and it's not like the whole nation found out and voted him back in anyway, in fact no one knew about David and Bath Sheba, other than God and Nathan the Prophet. God forgave him after he repented when Nathan confronted him, but there was still a price to be paid, his son by Bath Sheba died. Jacob had some shady dealings I admit, but again, he seemed to outgrow them over time and his position as leader was based on the birthright being passed to him by his father, and that was that. Soloman, ditto, King when he married pagan wives, King when he died. No one had to discern whether to give them power back, they had it.
Moses killed an Egyptian slavedriver, among the people (the enslaved Jews in Egypt) he led his murder was something which, rather than being viewed as a negative, was in all likelihood a feather in his cap, so not really analogous. As for Paul, I am pretty sure the New Testament makes specific mention that a number of Christians didn't trust Paul for a quite a while after his conversion.
EDIT: As Tennrich1 points out, David did not inherit the throne by heredity, however he WAS already King when the incident with Bath Sheba occurred, he already had power, it is not an example of some group of people giving him power back. Again, no one even knew about it other than Nathan and God. God is the only person who could have taken his power, and God's judgment, unlike ours, is again perfect. He knew David's repentance was true.
