No private keys for address?

I did a stupid thing. I deposited USDC on Polygon to Kraken, but they only support it on Ethereum.

I feel stupid of course (I’ve done tons of transactions and always get nervous - but never has something actually gone wrong)…

I then texted support about it, thinking they could maybe recover it using their private keys (which of course they can’t / don’t want). But something the support guy wrote irritates me:

„When a deposit is sent on the Polygon Network to a standard Ethereum address, the private keys would need to be exported and then imported into a Polygon Network wallet in order to recover the funds. However, this is not possible with our ERC-20 deposit addresses, as they are generated using smart contracts on the Ethereum blockchain. Addresses generated this way don’t have private keys associated to them, therefore we have nothing to export.“

Is this really possible? Creating address as smart contracts and not having the private keys? Or am I understanding this wrong? This doesn’t necessarily have to do with the original problem, I‘m just curious.