Is it possible to infer from the hadiths of Mu'adh and the Fear Prayer the permissibility of an obligatory prayer being performed behind someone performing a supererogatory prayer, given the difference between the intention of the one performing the supererogatory prayer in the two hadiths (performing an obligatory prayer that he had previously performed or leading an obligatory prayer) and the scenario of the question (the intention of the one performing the supererogatory prayer is to perform a purely supererogatory prayer)?

This website chooses the preponderant opinion and supports it with evidence. The issue at hand is a matter of scholarly disagreement. Sheikh al-Islam Ibn Taymiyyah and the scholar mentioned in the question have issued fatwas in line with the Shafi'i madhhab (definition). Therefore, agreement with the Imam in the intention of a fard (obligatory) or nafl (supererogatory) prayer is not obligatory, and the Imam is a guarantor even if he is praying a supererogatory prayer. It has been reported from Jabir that Mu'adh used to pray Isha with the Prophet, peace and blessings of Allah be upon him, and then pray it with his people; it was a supererogatory prayer for him and an obligatory one for them. This is an authentic hadith (definition). Al-Bayhaqi affirmed that the addition "it was a supererogatory prayer for him and an obligatory one for them" is acceptable and that it is from the saying of Jabir, and that the Companions would not say such a thing except with knowledge. The Prophet, peace and blessings of Allah be upon him, only criticized Mu'adh's action for its prolongation.