No, you were not right.
It seems you misunderstand something.
Read my response again:
You don't need to know the private key.
When the output is being spend, the unlocking script has to be revealed. And once you observe this, you can tell whether it is P2WPKH nested into P2SH or a multisig P2SH. Or even something completely different.
However, if the UTXO is not spent yet, there is no way of knowing this other than having the unlocking script created by yourself (i.e. you are the recipient).
So, to summarize and to reference your statement:
1) You don't necessarily need the private key. Observing the unlocking script being published (a.k.a. the output is being spend) is enough.
2) Even if you made the transaction creating the UTXO, you don't know anything about the unlocking script.
As a sender, you just use the address provided by the recipient to to create that new UTXO. You, as a sender, don't know wheter this is multisig or P2WPKH nested into P2SH. It is irrelevant whether you or someone else created the transaction/UTXO.