Did you read today's article about multiple ovulations during a single month? It looks like there could be more reasons why they "fail" than just "cheating."
Yes, I did ... it's old news. And if the couple is following all the NFP rules (this situation is covered by the instructors and in the book, if i remember correctly), they'd be able to catch the double ovulation.
Actually, the sympto-thermal method would likely catch this. It would reduce "safe" days for sexual activity to a pretty small amount though. Something like 2-3 days per month, not necessarily in a row.
However, as a former practicioner of NFP, I'm more in agreement with your previous statement that, "I put the word 'success' in quotes because I do not consider it a success when a couple avoids having children."
NFP is too often used as a Catholicized enabler of the contraceptive mindset. Probably safest for all but those in dire need to avoid.