While it's true that Chase cards are all Chip & Signature, it's nearly impossible that entering a PIN in a POS machine would magically convert a purchase into a cash advance. I realize that's what you were told, but it's beyond implausible.
Since it involves a bank trying to find ways to get more fees from a customer, I'd say that it's entirely plausible.
Why do you believe that this isn't possible? It's just a matter of how the transaction is processed. It's possible that the system could try several different types of transactions before eventually hitting the POS option.
There may be policies/guidelines in place that describe how cash advance transactions are supposed to be processed, and likely including some explicit approval from the person making the purchase, but it wouldn't be the first time someone didn't adhere to the merchant guidelines.
Or are you saying that there's a technical limitation here that prevents this from happening?