There's some direct influence between the two -- a lot of Western occultists in the late 19th and early 20th centuries eagerly read translations of Hindu writings -- but that only became an option because the basic assumptions and worldviews of the two teachings were so similar from ancient times on. Thus, like you, I treat the similarities as evidence for the truth of those common teachings -- not least because Western occultism had to survive for so many centuries in an environment in which being caught thinking like a Hindu was grounds for a very painful death. If there hadn't been some very real reason to hold to those beliefs, I doubt they'd have kept springing up over and over again...