Here's my honest two cents... This sort of stuff is usually found during background checks. IRCC doesn't just guess that someone is married. They determine this based on actual documentation. I think your wife needs to think back to those four years and really rack her brain if there is any legal document where she may have listed herself as married (tax return, property or rental agreement, something employment related, etc.).
How long do you have to respond?
I trust info from scylla.
I was trying to see if Korea could be where de facto marriage become de jure marriage. Hence the mistake. It could still be an IRCC mistake of course
But then the Canadian website information supports what scylla wrote. Which doesn't make sense to make such a glaring mistake.
Anyway for the OP I truly hope that it is a case of IRCC making a mistake.
Wish you all the best.