[not a teacher]
I think you're correct with "caught red handed". Also, in the US, IIRC I've only ever heard "dead to rights".
This appeared in the Yahoo news story Ex-UK official: Spies did use fake rock in Moscow.
"There's not much you can say, you can't really call up and say 'I'm terribly sorry about that, it won't happen again'. I mean, they had us bang to rights," said Powell, Blair's chief of staff throughout his decade in office.
What does 'they had us bang to rights' mean? Is it the same as 'they caught us red handed'?
I have not heard the 'dead to rights' which BobSmith mentioned, but there are a lot of idioms in the English language. 'Bang on' means absolutely right, so 'bang to rights' essentially means 'we were caught correctly', but this isn't a phrase which would be used in everyday language. 'Caught red handed' usually would mean something was illegal or not right, whereas 'bang to rights' is a much more informal way of saying something was wrong. For example, someone would be 'caught red handed stealing something', but I could be caught 'bang to rights' for using incorrect grammar. Wrong, but not as wrong as stealing.
However, in this instance I suspect it is a way of using a phrase to 'play down' the severity of the wrong doing, whilst still admitting that they were wrong.
If you're caught bang to rights, there's no way of avoiding it or getting out of it and no excuses to be made.
Thank you all for your responses and explanations.