Yes, but for that there would have to be no fraud. You can't know your error rate without having some known errors. Otherwise you may well be simply blind to the fraud that you do have but are not aware of.

That fraud by itself is not beneficial goes without saying.

That is true, but it also tends to make the original statement meaningless. Now you're saying that (1) "in order to detect fraud, you have to have some fraud", and (2) "everyone everywhere, with no exceptions, has some fraud". This means there is no requirement for being able to detect fraud that is not automatically satisfied by everyone. Why bother talking about a requirement that is automatically satisfied?

Because it is the degree of fraud that you catch that matters. Every financial system has fraud. In the old days - I used to work at a bank - the banks knew that there was fraud, but usually they didn't have a really good grip on how many of their transactions were fraudulent and how much of that they caught. The limitations on human resources alone made this a losing battle.

Just like any classification system a fraud control system has false positives, false negatives, true positives and true negatives. In an ideal version of such a system you have no false positives and false negatives. But that idealized version of that system (the one that perfectly classifies fraudulent transactions and non-fraudulent transactions) is static. It can't adapt to cases of fraud that it hasn't seen yet. Eventually a fraudulent transaction gets through.

And that transaction if not detected timely but after the fact (so now there is some fraud) will result in an update to the fraud detection system (probably it will need more than one example to be able to generalize from). Now the perfect system may start to generate false positives or false negatives on other transactions.

So that's why all of this is relevant. I hope I'm able to explain it clearly enough.