The Purple Hearts and the medals are just annoyances to them but the anti-war activity hurt them.
If he admits to being an informer, the anti-war crowd will turn on him. He can't afford to do that. Personally, I don't think he was an informer -- that would have required intelligence on his part.
No, he wound need to correct the record and the left would dump him.
I don't think him being an informant is the case however.
At one point I also wondered if Kerry might have been an informant. But, like you said, he surely would have announced this when the ads appeared, and it doesn't make sense that he would save this for an October surprise.