She did not get rejected for that reason alone, perhaps she misunderstood the notice. Anyone applying for TANF must attempt to receive support from an absent relative before receiving the benefit. The state will pay for up to 3 paternity tests per child. It is important to establish paternity for reasons beyond financial benefit (medical history, etc). There is an exemption if doing so would put the family at risk for domestic violence or if the child was conceived due to rape. Should your friend choose not to pursue support she can still qualify if otherwise eligible however the grant is reduced by 25% for failure to cooperate with support requirements.

There's no way to be sure except to be thorough. State her case honestly, have testimony or statements from others as proof she has no info on the fathers.