EITC Tiebreaker

According to EITC rules, a child is qualifying for her mother and brother. Her brother has a SSN and is eligible for EITC. Her mom has an ITIN and is not eligible. Her mom's AGI is more than her brother's. Tiebreaker rules for a Qualifying Child of More than One Person assign a child to her parent over other relatives. If parents do not claim her they allow others to claim her only if their AGI is higher than the parent.

 

Does the tiebreaker apply when she qualifies for more than one eligible person or simply when she qualifies for more than one person? If both conditions must apply then the brother can claim her otherwise no one can.