It’s not a threat; they’re telling you how their system normally works. Chargebacks are automatically flagged in PSA’s system when the issuing bank takes the funds back.
If the payment was never received by PSA, the card issuer will find that during their research of the transaction. They will put the funds back into your available balance. Since it shouldn’t be taken from PSA, there shouldn’t be a chargeback flag.
The disput process isn’t an automatic reversal. The bank will issue a provisional credit while they continue to research the transaction. It’s a federal regulation they are following; “Reg E”. You’ll get a permanent credit at the end when they determine what went wrong. The research includes contacting PSA’s bank to figure out what went wrong.
It sounds like both the customer service agent and you are only able to provide information about this that is available first-hand to you both. Since neither of you have the full picture of what has actually happened, you are both arguing things from your perspective. Neither of you are 100% wrong, but neither of you are 100% correct also.
There is no malicious intent of fraud on PSA’s behalf.
Again, this is a common occurrence in banking. Just dispute the transaction so the bank can put back your money.