Perhaps for Kṣatriyas, it is a mandatory injunction, as a part of their "Varṇadharma", to not dismiss an "approaching girl", but such an injunction doesn't seem plausible and valid for the other Varṇas.
We can verify this from this excerpt from the Śrīmad-Bhāgavatam Purāṇa when Śarmiṣṭhā begged King Yayāti for a son.
राजपुत्र्यार्थितोऽपत्ये धर्मं चावेक्ष्य धर्मवित् । स्मरञ्छुक्रवच: काले
दिष्टमेवाभ्यपद्यत ॥ ३२ ॥
When Princess Śarmiṣṭhā begged King Yayāti for a son, the King was
certainly aware of the principles of religion, and therefore he agreed
to fulfill her desire. Although he remembered the warning of
Śukrācārya, he thought of this union as the desire of the Supreme, and
thus he had sex with Śarmiṣṭhā.
In the purport to the above verse, Śrīla Prabhupada also verifies this injunction for the kṣatriyas.
King Yayāti was completely aware of the duty of a kṣatriya. When a
kṣatriya is approached by a woman, he cannot deny her. This is a
religious principle. Consequently, when Dharmarāja, Yudhiṣṭhira, saw
Arjuna unhappy after Arjuna returned from Dvārakā, he asked whether
Arjuna had refused a woman who had begged for a son.