How can the Hadith about the Prophet (peace and blessings be upon him) not returning the greeting of Salām until he performed tayammum be reconciled with the Hadith "He (peace and blessings be upon him) used to remember Allah at all times"? And is it permissible for someone in a state of major ritual impurity (junub) to recite the Qur'an by analogy with that?

Summary: The Hadith of Abu Al-Jaheem indicates the desirability of remembering Allah while in a state of purity. Hence, the Prophet, peace be upon him, performed tayammum to return the greeting for fear of missing it, not as an obligation. As for the Hadith of Aisha, it indicates that the Prophet, peace be upon him, remembered Allah at all times except in the state of ritual impurity (janabah), based on other evidence that prohibits a ritually impure person from reciting the Quran. This is what the majority of jurists have concluded.