I don't think the 6 month thing is anything you can rely on.
If they find the records and present them for payment next year, what are you going to do ? Ring your provider and say that you did authorise the payment, and you did use the flights, but that was, like, you know, years ago . . . and you shouldn't have to, like, pay.
Unlikely.
Most people would end up paying because they recognise that they owe the money.
This is not to say that most people would chase down the merchant and say "Oi, I owe you three and a half grand, please take it from me." Apart from anything else you would run the risk of being charged twice - once when you volunteer and again when they eventually find the record.
I say you just sit tight, stick some emergency money away to cover it just in case it does come through and eventually (after 1/2/3 years) decide they are never going to come after the money and have a few beers on them. Depending on whether you are feeling lucky or not, you could go for double or quits and book another ticket with them . . .
z