Here we go again
... when Bob lost the argument about p-c parity ... he claimed he just wasn't interested in the debate any more
He didn't lose. You didn't understand his very accurate, informative response. I suggest you try reading what he wrote again and digest it this time.
Of course, you may be confusing p-c parity with non-arbitrage
... but that is a different subject
You are getting cute w words. Most likely saying the same thing.
P/C parity always holds. I won't be jumping into your hypothetical as your perspective and facts are both flawed.
The difference is always some extra risk being priced into p vs c. Early exercise plus cost of carry plus extreme market conditions can do some bizarre things to markets . Shocking, I know

If you want to point me to a product, id be happy to explain what's happening. I would need to know the product, all bids/offers for every p/c as well as the underlying, to give you a high school level explanation.