How finding a working nonce says anyting about the validity of an initial transaction
Finding the nonce and computing Proof of Work is unrelated to transaction validation. Locking blocks together in a chain of expensive Proof of Work ensures that is expensive to replace the current ledger/ blockchain with an alternative.

Further, transactions do not contain information about blocks or Proof of Work. Validation of transactions is achieved through the use of Elliptic Curve cryptography. Specifically, an Elliptic Curve Digital Signature Algorithm (ECDSA) over the curve secp256k1.

The mathematics of ECDSA ensure that only those who know the private key can generate valid signatures. However, any one can use the public key to verify that a signature was produced by somebody who has knowledge of the private key.

Lastly, to ensure that unspent transaction outputs (UTXOs) are not double spent, the Bitcoin protocol dictates that a block is invalid if it includes a transaction which references a specific UTXO as an input which has previously been referenced in a transaction input before.