"Is this actually good advice?"
No. Penalties will continue to accrue every year until the excess is resolved, an resolving in a later year by making a regular taxable distribution will results in double taxation and a 20% additional tax on the amount distributed.
It's odd that the HSA custodian would not pay the corrective distribution to your daughter. It's your daughter's account, after all. The HSA custodian should only pay the distribution to the former employer if the former employer makes the request.
If the HSA custodian is uncooperative, it's possible that your daughter could trustee-to-trustee transfer the account to a more cooperative HSA custodian and make the corrective distribution from there. However, this creates a complication in that the new HSA custodian will not be able to calculate the net income attributable to the excess and instead would have to rely on your daughter (or someone like you on her behalf) to do the calculation and indicate how much is excess and how much is earnings.
Another option would be to do the calculation of the attributable earnings, take the amount as a regular distribution before the due date of the 2024 tax return, then paper file your daughter's 2025 tax return with an explanation that the Form 1099-SA issued by the HSA custodian reporting a regular distribution is incorrect. However, this is almost certain to raise a red flag with the IRS because the IRA automated under-reporter system should detect a discrepancy.
