Tax Question How is dependency determined by the IRS in cases of joint custody, if the agreement is only verbal? ? (Details inside)

My daughter, who is now single, claims her daughter as a dependent. She provides the majority of the funds necessary for her upbringing. She provides the education, medical care, insurance, housing, the vast majority of the clothing, child care on holidays and during the summer. She has all the paperwork associated with all of it. Since, however, she and her ex pretty well split the time with their daughter 50/50 the day to day expenses such as food and transportation are paid by the individual parent.
This has been going on for about four years although the 50/50 time split is only about a year or so old. About four years ago, when she provided the majority of the care it was decided that she would claim their daughter. This was entirely verbal however.
She recently found out that her ex has taken to also claiming her daughter as a dependent.
Being as it appears they are both claiming her, if the IRS comes after him, will they also come after my daughter?