Is she concerned about it, or is she being bullied by her ex who thinks it's a problem?

Why would IRS tell people to do this in Pub 501 if it weren't a common situation, covered in the first day of tax class?

" If the child who qualifies you for
this filing status isn't claimed as your dependent
in the Dependents section of Form 1040 or
1040-SR, enter the child's name in the entry
space at the bottom of the Filing Status section. "