I have to agree with the others here about German cars. I started out with Volkswagons, saw the light and had Toyotas, then thought I'd treat myself to a 5 Series BMW CPO car. Total disaster, and I made myself a promise to NEVER PURCHASE ANOTHER GERMAN CAR AGAIN!!! Skeptical? Go down to your library and ask to see the most recent annual new car issue of Consumer Reports magazine. See what they have to say, especially about VW and the Passat. Maybe if you'd have done that to begin with, you're fiance would be driving a Toyota or Honda now. Yeah, 20/20 hindsight. Sorry.
I have a hard time believing that an anti knock sensor would put a car into limp home mode. ****** the timing, yes. You might notice some sluggishness, but not the symptoms you're experiencing. When the used car dealer gets the car back, go down to the VW dealer first and ask to speak with the service manager. Explain the situation to him, and see if he provides a reasonable rationale for the repair that was made. Also inquire if there is any warranty associated with that repair, and about whatever warranty may be left on the car. You might as well try to build some rapport with the dealership now, because if my experience is any guide, you'll be seeing a LOT of him if you get stuck with the car. That is, unless, you can find a GOOD independent. If you can, it might even be worth while to take the car to him for an inspection, which should have been done prior to the purchase. Sorry, again more 20/20 hind sight.
It may be too late now, but see what the BBB and rating services like Yelp have to say about the used car dealership that sold you the car. If they have addressed the complaints against them satisfactorily, chances are they'll do the same for you. If not, I'd insist on a refund, even if it cost me some money to do so. After all she's driving a free rental now, and it is reasonable to reimburse the dealer for that cost. If the dealer checks out OK with the BBB, I'd still ask for a refund. Your fiance has been traumatized by her delivery day experience and will never ever trust that car. Any little squeak or lurch will have her heart in her mouth, and she'll cringe every time she drives it. If the dealer refuses a refund, ask if they'll give you credit toward something else on the lot. Here's where your trip to the library could pay off. See if they have something with good CR ratings, and ask for a free CarFax report. I also agree with others that a clean CarFAX is no guarantee, but if something obvious shows up you have a chance to pass. If you get that far, the dealer should be willing to bend over backwards to make you a great deal. Go armed with prices from Cars.com and other on line sites, and don't forget to check Craig's List to see what's on the market locally. Keep in mind that for sale prices are often 30% above what dealers customarily allow on trade ins or their purchase cost on cars. Ask for, no, insist, on an extended warranty. The dealer's cost on these is almost nothing, and having one is better than nothing. Before you agree to a deal, research the warranty company on line and see if it's legit, as this is another area ripe with problems. You can do this while you have the car inspected by a trustworthy independent mechanic. If the dealer balks at any of this, make it clear that you've consulted an attorney, and while you'd hate to initiate legal action, you'll do so without hesitation if you feel you're being treated unfairly or dishonestly.
Also keep in mind that by the time a car gets onto a dealership lot it's already been rejected by many other potential buyers, and unless that dealership has a means to effect repairs at rock bottom prices, chances are those problems are going to be coming to the new owner as part of the deal.
I hope the situation works out for you, but honestly I'm not optimistic. It all hinges on the integrity of the used car dealer, and they haven't earned their notorious reputation by being angels.