Regarding Vanguard, the question was not how the account was titled, which seems correct, but was whether Vanguard would be reporting on Form 5498 receipt of any kind of contribution. If Vanguard reports any kind of contribution on Form 5498, that would be an additional problem, but is probably unlikely since Vanguard would likely have known that they could not accept an actual rollover into this newly established inherited IRA.
I have a family member who had a similar experience due to the bank local-office rep simply marking the wrong box on their form for moving funds out of one IRA into another, despite repeated insistence that this was to be a transfer, not a distribution. In that case this bank was even the custodian of both accounts, not involving any outside coordination! It took months to get a correction, with the bank finally properly issuing a corrected Form 1099-R identical to the original except with all dollar amounts replaced with zeros. This is the same correction that you need to obtain.
