For Hindus, Buddha was just one of the 10 avatars of Vishnu and he came for a time and purpose. It was never meant to be a separate religion but just took Hindu teachings on meditation and enlightenment and got adapted into another "ism". All the core teachings lie in Hindu scriptures, including Yoga, Meditation etc.
For Hindus, claiming everything in the subcontinent as their own seems like a favorite passtime. Jainism, Buddhism are not part of Hinduism and never were.
I think most people would agree that Buddhist doctrines first originated within a Hinduism-informed general milieu, and they can only be understood comprehensively in this light. Whereas Jainism seems to have developed in parallel with Vedic religion, and to have shared some of the same underlying concepts. Whether this means either are "part" of Hinduism probably depends on whom you ask.
What does "scripture" mean in this context? Scripture normally means messages 'directly' from the 'Abrahamic God' received by certain 'special individuals' (prophets, etc), such as the Bible, Quran, Torah. I thought Hinduism did not have any belief in any messages being sent from "God" to humans. So could you give some examples on what would be Hindu scripture and other examples of what would NOT be Hindu scripture?
And Hindu scriptures is the example the lexicographers chose. Besides, the Old and New Testaments are traditionally attributed to specific authors. Only the Quran qualifies as scripture by your definition, not even the Hadith.
> I thought Hinduism did not have any belief in any messages being sent from "God" to humans.
The Vedas are considered revelation from the ultimate reality. There are other scriptures considered apauruseya i.e. of non-human origin.
> The Vedas are considered revelation from the ultimate reality.
As far as I can tell from googling, they are just considered to be stories from Aryans that entered India. "The Vedas are considered the earliest literary record of Indo-Aryan civilization"
> As far as I can tell from googling, they are just considered to be stories from Aryans that entered India. "The Vedas are considered the earliest literary record of Indo-Aryan civilization"
"Tradition has it that humans did not compose the revered compositions of the Vedas, but that God taught the Vedic hymns to the sages, who then handed them down through generations by word of mouth. Another tradition suggests that the hymns were "revealed," to the sages, who were known as the seers or “mantradrasta” of the hymns."
According to Shahrastani some Muslims had pretty positive views of Vedas. Moreover Dara Shikoh famously considered Upanishads the “guarded tablet” mentioned in Quran 85:22