Yes that's mostly true of Hinduism today, but only because 5 schools (of the 6 main ones) have diminished. The Vedanta school is prevalent today, and that one relies on Vedas (of which Upanishads are a part). But, for example, the Yoga school is fully empirical (i.e. first person experience) and doesn't rely on Vedas or any writings for its philosophy. Their teachings are mostly techniques or experiences of previous gurus to get to the stage of realizing the truths for oneself.
There are schools of thought including both, and a whole lot more, and many terms have no English equivalents. This does a decent job: https://en.wikipedia.org/wiki/Indian_philosophy
Hinduism (at least originally) is a catch-all term for indigenous traditions, rather than a tradition itself.
Yes that's mostly true of Hinduism today, but only because 5 schools (of the 6 main ones) have diminished. The Vedanta school is prevalent today, and that one relies on Vedas (of which Upanishads are a part). But, for example, the Yoga school is fully empirical (i.e. first person experience) and doesn't rely on Vedas or any writings for its philosophy. Their teachings are mostly techniques or experiences of previous gurus to get to the stage of realizing the truths for oneself.