SANA, Yemen — To hear the Houthi militants who control this capital describe it, the country’s former president escaped from house arrest on Saturday by dressing as a woman, wearing a long black chador covering all but his eyes.

One Western official recounted a story he had heard: that the leader then climbed into a food truck, negotiating the Houthis’ scores of armed checkpoints through the capital and along hundreds of miles of highway undetected amid frozen meat.

Alternatively, all of that was just so much face-saving spin, in the view of many observers here, and the Houthis, possibly with tacit support from the United Nations, simply allowed the former president, Abdu Rabbu Mansour Hadi, to leave his home as part of the negotiations to reach a political agreement among the country’s feuding parties.

Whether he escaped or was let go, by the end of Saturday, Mr. Hadi was in his hometown, Aden, in southern Yemen, where anti-Houthi and secessionist sentiment runs strong.