Frankly, all your quote shows is that there are some circumstances under which people can choose who claims the child as the qualifying child. It doesn't get into what those circumstances are.
I pulled the following from Publication 17, which is where your quote appears to originate from:
If the parents don't file a joint return together but both parents claim the child as a qualifying child, the IRS will treat the child as the qualifying child of the parent with whom the child lived for the longer period of time during the year. If the child lived with each parent for the same amount of time, the IRS will treat the child as the qualifying child of the parent who had the higher adjusted gross income (AGI) for the year.
Example 8—Separated parents.
You, your husband, and your 10-year-old son Joey lived together until August 1, 2018, when your husband moved out of the household. In August and September, Joey lived with you. For the rest of the year, Joey lived with your husband, who is Joey's father. Joey is a qualifying child of both you and your husband because he lived with each of you for more than half the year and because he met the relationship, age, and joint return tests for both of you. At the end of the year, you and your husband still weren't divorced, legally separated, or separated under a written separation agreement, so the special rule for divorced or separated parents (or parents who live apart) doesn't apply.
You and your husband will file separate returns. Your husband agrees to let you treat Joey as a qualifying child. This means, if your husband doesn't claim Joey as a qualifying child for any of the tax benefits listed earlier, you can claim him as a qualifying child for any tax benefit listed earlier for which you qualify. However, your filing status is married filing separately, so you can't claim the EIC or the credit for child and dependent care expenses. See Rule 3.
At first blush, it does seem like the IRS is administering the law the way Frankly says. But does this indicate the IRS will always allow the parents to choose? Is there some basis for this position somewhere?
Wondering this, I re-read the statute I cited earlier (underlines added):
(B) More than 1 parent claiming qualifying child If the parents claiming any qualifying child do not file a joint return together, such child shall be treated as the qualifying child of—
(i) the parent with whom the child resided for the longest period of time during the taxable year, or
(ii) if the child resides with both parents for the same amount of time during such taxable year, the parent with the highest adjusted gross income.
It looks like this can be read so that it's only invoked when two conflicting claims are made at the same time.
What do you think, HowardS? Were we wrong about this?