What should one do who entered the Dhuhr prayer having missed two or three rak'ahs, and doubted that, so based his action on his certainty that he had missed two rak'ahs, and thus made them up and performed the prostration of forgetfulness (sujood as-sahw), then later remembered that one rak'ah remained for him?

What you did by building upon the least and then completing the prayer and performing the prostration of forgetfulness is correct. However, if you are certain, then do not pay attention to the man's words. If you are not certain, then complete your prayer; if you do so, it is good. But if you did not complete the prayer and there was a prolonged interruption, then you must repeat the entire prayer.