Assuming that the check with the funds from the traditional 401(k) account did not specifically identify the traditional IRA as being the recipient, it appears that the IRA custodian did not make a correctable mistake and the resulting rollover to the Roth IRA cannot be undone. This makes the rollover taxable.
I agree that the 401(k) plan has no obligation to change the code-G Form 1099-R be cause this was not their error (although I don't think the second reason they give is correct because I believe they are legally obligated to offer a direct rollover from the traditional 401(k) account to a Roth IRA). Under these circumstances, you'll need to enter a substitute Form 1099-R (Form 4852) replacing the zero in box 2a with the correct taxable amount and provide explanation for the change.
