You are right. There is a wiki article that we can see an philosophical statement of it, it is clearly that mahayana and vajrayana have a foot in foot in vedic culture. Thats why academic study of them is hard, the scholar has to research in hinduism to undertand many things. Also, in my view, some may do not agree with it but We westerners that have a greek/roman (Socrats,Platos, Aristoteles, etc.) like mind with the system of sientifical proof and analytical study, it is hard to accept as truth, in the first contact, something like buddha fields, celestial boddhisattas, buddha nature, rituals, etc. Theravada has preserved all or almost if not all, the early Buddhist Saramanas thoughts as it was thought by the Lord and it is an analytical system and has scientific principles.
Indian philosophy is a confluence of Śramaṇic and Vedic streams that co-exist and influence each other. Śramaṇas held a pessimistic world view of samsara as full of suffering (or dukkha). They practiced Ahimsa and rigorous ascetism. They believed in Karma and Moksa and viewed re-birth as undesirable.
Vedics, on the contrary, hold an optimistic world view of the richness of worldly life. They believe in the efficacy of rituals and sacrifices, performed by a privileged group of people, who could improve their life by pleasing certain Gods. The Sramanic ideal of mendicancy and renunciation, that the worldly life is full of suffering and that emancipation requires abandoning desires and withdrawal into a solitary contemplative life, is in stark contrast with the Brahminical ideal of an active and ritually punctuated life. Traditional Vedic belief holds that a man is born with an obligation to study the Vedas, to procreate and rear male offspring and to perform sacrifices. Only in later life may he meditate on the mysteries of life. The idea of devoting one's whole life to mendicancy seems to disparage the whole process of Vedic social life and obligations. Because the Sramanas rejected the Vedas, Brahmins labelled their philosophy as "nastika darsana" (heterodox philosophy).
Beliefs and concepts of Śramaṇa philosophies:-
Denial of creator and omnipotent Gods
Rejection of the Vedas as revealed texts
Affirmation of Karma and rebirth, Samsara and transmigration of Soul (Later these practices were accepted in Brahminic religion Hinduism)
Affirmation of the attainment of moksa through Ahimsa, renunciation and austerities
Denial of the efficacy of sacrifices and rituals for purification.
Rejection of the caste system
Ultimately, the sramana philosophical concepts like ahimsa, karma, re-incarnation, renunciation, samsara and moksa were accepted and incorporated by the brahmans in their beliefs and practices, eg. by abandoning the sacrifice of animals. According to Gavin Flood, concepts like karmas and reincarnation entered mainstream brahaminical thought from the sramana or the renounciant traditions. According to D. R. Bhandarkar, the Ahimsa dharma of the sramanas made an impression on the followers of Brahamanism and their law books and practices.
Following are the two main schools of Sramana Philosophy that have continued since ancient times in India:
Buddhist philosophy is a system of beliefs based on the teachings of Siddhartha Gautama, an Indian prince later known as the Buddha. Buddhism is a non-theistic philosophy, one whose tenets are not especially concerned with the existence or nonexistence of a God or gods and which denies the existence of a creator god. The question of God is largely irrelevant in Theravada Buddhism, though most sects of Mahayana Buddhism, notably Tibetan Buddhism and most of East Asian Buddhism (in the Shurangama Mantra and Great Compassion Mantra) do regularly practice with a number of gods (as Dharmapalas and Wrathful Deities, Four Heavenly Kings, and Five Wisdom Kings) drawn from both the Mahayana Sutras and Buddhist Tantras sometimes combined with local indigenous belief systems. The Buddha criticized all concepts of metaphysical being and non-being. A major distinguishing feature of its philosophy is the rejection (anatman) of a permanent, self-existent soul (atman).