If remember correctly there was a case of a saudi national a few years back (post 9/11) who did a re-currency in the US without visa and was subsequently banned for life to enter again after being deported.
However, I'd also like to get the most recent rules as I will go to the US for a type rating in the next couple of months.
In the past I have done all my flight reviews without a visa but I guess why take the risk.