Thanks for the additional details. They tie all of the previous information together.
If this inherited IRA was truly moved by trustee-to-trustee transfer, the old custodian should not have issued a Form 1099-R. You need to fight this with the old custodian because the Form 1099-R the old cusotdian issued implies that that the money was paid to you, not paid directly to the inherited IRA at Vanguard and a distribution paid to you is not eligible for rollover to a different inherited IRA. You'll also want to verify that Vanguard has treated this as a nonreportable transfer and will not appear as a rollover on Form 5498 for the new account.
Note that some versions of 2020 TurboTax will allow you to report this as a rollover even though in this case a rollover is not permitted. This has to do with the IRS permitting repayment back to the original IRA of amounts that would have been an RMD were it not for the CARES Act, but that doesn't apply to your situation.
If the old custodian happens to be a bank rather than a larger financial institution like Vanguard, my experience is that front-line reps at banks are notoriously bad at understanding these nuances. Regardless, make sure that you escalate the issue to the back office personnel responsible for IRAs who might know a bit more about this. If Vanguard has understood this to be a nonreportable trustee-to-trustee transfer, it seems that they would not have accepted the transfer without believing that the old custodian was also treating it as a trustee-to-trustee transfer. Trustee-to-trustee transfers generally require coordination directly between the custodians to ensure that mistakes do not happen on either end.
