As a former employee of a very well-known, very high-end department store chain I have first person knowledge of the fact that shoppers are very often "known" but not as often "outed".
As employees and sales associates we only wanted it to be reported that we had a perfect shop, and didn't want to let on to the shopper that we were fully aware that they were performing a scenario that we had read about, heard about and even practiced in order to ensure that we received a perfect score when it was our turn. We were all aware that we were shopped at minimum once a quarter, and often more than that.
The upside to this from the client standpoint is that we practiced being so customer oriented and so aware of what "might" be asked that it became second nature to use that attitude, language and completeness to any and all transactions. It didn't matter that it was a shop, it was just our business as usual.
We also had incentives tied directly to our shopper scores. These ranged from additional compensation, gift cards, dinners and movie tickets. Our department's were evaluated and incentivized by how we did as individuals and collectively. It was in all of our best interest to know who was "maybe" shopping us, what they would ask, what they might say to "trigger" our scripted follow-up and what they might do to throw us off. From a management standpoint, it was a great opportunity for continuing education and improvement as the practice shops were more rigorous than any that were actually done by the mystery shopper.
I personally don't have a problem with the idea that they "might" know who I am, and/or that they can breath easy and high-five once I'm gone having found the "shopper" and hit all of their points correctly. I haven't had a single shop denied for being "outed" and it seems unlikely from my experience the last few years doing rotation shops.
I hope that this happens as the usual, instead of the unusual when they want the shop dropped for sub standard performance and perhaps claim that they "knew it was a shopper therefore"