Most of their sacred or quasi sacred texts make no claim of divine inspiritation. Not the Dhammapada, Analects of Confucius, Pirqe Aboth, Nihongi, Kojiki, Tao Te Ching or Chuang Tzu.
That leaves the Bhagavad Gita and the Qur'an. I seriously doubt the Qur'an claims divine inspiration, though I have seen a surah interpreted as such.
And if you are in doubt about what We have sent down upon Our Servant [Muhammad], then produce a surah the like thereof and call upon your witnesses other than Allah, if you should be truthful.
Allah sent the sura to Muhammed and none but Allah can produce a truthful sura.
And [recall] when We gave Moses the Scripture and criterion that perhaps you would be guided.
The Torah was also directly given to Moses by Allah.
And We did certainly give Moses the Torah and followed up after him with messengers. And We gave Jesus, the son of Mary, clear proofs and supported him with the Pure Spirit. But is it [not] that every time a messenger came to you, [O Children of Israel], with what your souls did not desire, you were arrogant? And a party [of messengers] you denied and another party you killed.
Allah gave the Torah to Moses and the 'signs'
Say, "Whoever is an enemy to Gabriel - it is [none but] he who has brought the Qur'an down upon your heart, [O Muhammad], by permission of Allah, confirming that which was before it and as guidance and good tidings for the believers."
Gabriel upon the instruction of Allah brought the Quran to Muhammed, confirming the Torah and the gospels.
Note also that all these, and indeed, much of the Quran, is written in first person. Ie. these are not the words of Muhammed, but rather Allah.
The Dhammapada does indeed not claim divine inspiration ... because Buddha has knowledge SUPERIOR to that of the gods. The gods worship HIM because he has escaped from the eternal wheel of death and rebirth which they, the gods, are unable to do.