No, the Proof of Funds application proposed in BIP322 does announce which UTXOs you hold. To prove your funds, you create a transaction with a dummy input on the 0th slot that makes the transaction invalid for broadcast, and then an input for each UTXO you want to prove ownership of. By signing for the inputs that spend your UTXOs, your statement proves ownership and implementing support for BIP322 signatures would only require minimal changes to any software that can already validate Bitcoin transactions.