I don't know what algos they use to detect fraud but being a veteran does not always mean there won't be fraud on your bank account. Remember, this is not about those five 10 dollar transactions you authorized, this is about that one 5 thousand dollar one that was the result of fraud. From their point of view, a false positive is much better than a false negative.
You want to show up with cash, not a check.
If you buy something online for example and you don't get it, you can call them up bitch about it and they refund you, and in worse case if they are jerks and you used your credit card you can dispute.
With bitcoin, once transfer is done from one account to another account, the transaction is not reversible. Since bitcoin addresses are anonymous, you don't know who it went to so there is no way to track and reverse the transaction like we do with refunds and voids.
However, his explanation doesn't make sense anyway. The concerns he raises are about fake accounts and having them to pay exchange to purchase the coins before they actually withdraw money from your account, which is taking a risk on their part to be able to secure the coins at the price you purchased. However, this is not true either. I had my orders cancelled back to back even if the money was withdrawn from my bank account. What risk? I don't know. Perhaps they made money from not granting me the coins that were doubled in price since last week.