Is it true if that were to happen, all I need is the private key to spend the funds?
Private keys are the means by which transactions are signed from corresponding addresses on the blockchain which were generated from they xpriv key. So, with the private keys you will be able to spend funds from that address.
If it were possible to generate private keys and public keys which has a balance on it, then it would not have been worth it, as the network would haveko value.