Is it true what was said that the Prophet, peace and blessings be upon him, said, "Satan is the third of them," and did not say, "Satan overcame them," and that based on this, seclusion between a man and a woman is permissible if they are confident in themselves and their faith?

It is not correct to interpret the Hadith (definition) as meaning that unlawful seclusion (khalwa (definition)) is exclusive to those who are not believers or do not trust themselves, because the Hadith is general and includes all men and women. Scholars have unanimously agreed on the prohibition of a man secluding himself with a non-mahram (definition) woman. Many Ahadith have been narrated to this effect, including the prohibition of a man spending the night with a previously married woman (thayyib) unless he is her husband or a mahram, the prohibition of a man entering upon a woman whose husband is absent unless he is accompanied by one or two other men, the prohibition of a woman traveling except with a mahram, and the prohibition of a man secluding himself with a woman.