Need help understanding Head of household rules when divorced

Hey all, I am recently divorced and my ex hired a tax guy and filed her taxes early this year. She claimed Head of Household and claimed child tax credit for our one child. We are flip flopping years on the child tax credit but had no agreement for head of household. Her tax guy told us that both of us could file for head of household. When I went to file, Turbotax seems to say differently. I read that it's supposed to go to whichever parent has the child more nights per year. We asked him for clarification and he sent this email below. Can you tell me if this is legit? Or semi-legit like it is a common wink wink nod nod thing people do because it doesn't get audited often? Or is he just terrible at his job?

RS Explanation for 1040:

To Whom It May Concern,

I will be filing as Head of Household, as I provide over half the costs of my home and meet IRS qualifications. However, I will not claim our child as a dependent, as my former spouse provides support per IRS rules. This ensures full compliance with tax law.

Overall Reply and Explanation from (name of the tax service):

Dear (my ex wife),

Thank you for clarifying your tax situation. You will file as Head of Household, and your former spouse will also file as Head of Household without claiming the child. Both arrangements comply with IRS rules. If any further questions arise, I’m happy to assist.

Reference Notes:

1. Head of Household Qualification:
   • See IRS Publication 501 (titled "Dependents, Standard Deduction, and Filing Information"). This publication details who qualifies as Head of Household and the support/residency requirements.
2. Dependent Claim Rules:
   • For dependency guidelines, refer to IRS Publication 501 (dependent section) or IRS Publication 17 (titled "Your Federal Income Tax"), which outlines who can be claimed as a dependent, considering factors like residency, support, and relationship.

These references will help ensure that all filing decisions align with current IRS regulations. As always, consult the most recent IRS publications or a tax professional for the most up-to-date information.

Sincerely,
(the tax guy)