Any time I hear "the dealer is saying" the hair on the back of my neck stands up. However, in this case there may be some merit to what they're saying.
The OEM Michelin PSS ZP tires are known to be subject to sidewall cracking if operated in close to freezing temperatures. The soft compound becomes brittle and, under initial load, they are known to crack the sidewalls. If you have driven the vehicle in near freezing conditions this may well be the case. The thing is, if the fronts show sidewall cracking, due to cold, it's almost certain that the rears would as well and, if so, the entire set should be replaced. This is where my suspicion of the dealer comes into play. If it were me, I would have all 4 tires checked by a reputable, trusted tire professional. Someone who is experienced with those specific tires. They will be able to tell you if the cracks are surface only, and are simply a result of natural aging, or if they are deep and structural in nature (cold cracking). If they are just surface cracks there's no need to replace them.
If your flat is a result of of a puncture in the tread section and less than 1/4" it can be successfully repaired with a proper plug/patch. If the damage is within the sidewall section it must be replaced. Again, a professional, high performance tire shop is your best bet.
The direct answer to your question is - if the sidewalls are cracked due to cold damage then yes, replace at least the 2 fronts if not all 4 tires. If the cracks are due to light, aged surface cracking you can replace or repair the punctured tire only.
Unfortunately, nascar03's offer won't help you as the GS tires will not fit your Stingray.
Best of luck
Ross