The TPM had multiple functions, and for verifying operating system images indeed no private key is required. For that to work, it is merely required that the OS

The TPM had multiple functions, and for verifying operating system images indeed no private key is required. For that to work, it is merely required that the OS doesn't have write access to the TPM. Private key material is required for remote attestation, which makes it possible to prove certain things to an external party, for example the exact identity of the TPM. This feature is much more questionable.