When nakowa first started winning big I spoke to an experienced gambling site operator about it. He told me words to the effect of "welcome to running a casino; that's how it is; you'll never be able to stop worrying about people cheating you". 
Steve Wynn used to quote something his father told him: The minute you stop watching a person in gaming, money sticks in the hands of angels.
In 1963, Steve Wynn's father died of complications from open heart surgery in Minneapolis, leaving $350,000 of gaming debts, shortly before Wynn graduated from Penn with a Bachelor of Arts degree in English. Wynn took over running the family's bingo operation in Maryland. His success allowed him to invest in a small stake for the Frontier Hotel and Casino in Las Vegas, where he and his wife, Elaine, moved in 1967. Between 1968 and 1972 he also owned and operated a wine and liquor importing company. He managed to parlay his profits from a land deal in 1971 (the deal involved Howard Hughes and Caesars Palace) into a controlling interest in the the Golden Nugget Las Vegas (which had been operating since 1946). I think he had to fire a third of the staff because they were cheating. It was so ingrained in the culture, that people would say I have to cheat, I don't make enough money.
But he also said that running on honest business helps in the long run. When he was in the wine and liquor business he had a good reputation. When he bought the casino one of his old customers called him up and said every day about a dozen of the employees from the casino come into my place to get drinks and divide up the chips they stole that day.
So I think your honest persona helped you with the 1300 BTC snafu. As near as I could tell about 95% of the investors were in favor of you simply rolling back the bets.
A friend of mine was dinged for double billing on his expense accounts for the military. He pleaded with the auditors saying it was just a clerical error on the part of his secretary, and if he was trying to cheat why would he submit paperwork that contradicted itself on one page. Basically the government changed procedures where instead of buying plane tickets on the credit card, they were bought through a central office. The secretary was unaware of the change, and listed the price of the plane tickets on the expense forms. But the auditors would not let him pay the mistake (with interest). Instead they had to drag him through the whole process so he would be denounced by name on the Senate floor. He not only had to pay back the money, but he was suspended from work for two weeks.