All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
There is nothing wrong with the person in a state of Janaabah following the funeral or burying the deceased, since the purity of either the major or the minor Hadath is not a condition for doing that. Rather, it is conditioned to offer the funeral prayer.
Perhaps the questioner misunderstood the Hadeeth narrated on the authority of Anas that they were in the funeral procession of one of the daughters of the Prophet, sallallaahu ‘alayhi wa sallam, and he was sitting by the side of the grave. I saw his eyes shedding tears. He said, "Is there anyone among you who did not have sexual relations with his wife last night?" Abu Talhah replied in the affirmative. Then the Prophet, sallallaahu ‘alayhi wa sallam, told him to get down into the grave. So he got down into her grave. [Al-Bukhari].
There is another interpretation of this Hadeeth that the Prophet,sallallaahu ‘alayhi wa sallam, meant (is there any one among you who did not commit a sin last night). However, the first interpretation does not necessitate the purity of both the major and minor Hadath to bury the deceased. Rather, it is recommended for the individual who buries the deceased to not have had sexual intercourse that night; the reason is that he is removed in time from pleasures as Al-Haafith Ibn Hajar said in Fat-h Al- Baari.
Allaah Knows best.