You haven't understood the crux of what I said. Buddhism and Jainism being branches of Sramana tradition is correct. The word Sramana itself originates from Taittiriya Aranyaka which is an annexure of the Vedas. Vedas are the basis for Hinduism.

Buddhism and Jainism are branches of Hinduism. Period. They are part of a group called Nastikas who don't believe in the Vedic rituals.