To be sure, a Western conception of Buddhism is likely to go astray. This is because the Western conception brings baggage to the task of understanding Buddhism (and Taoism, et al).
It might be worth unpacking this baggage. Western thought tends to divide the world into good and evil. At an abstract or general level, consider the idea of an amoral universe. In what sense is the universe amoral? In the same sense as an amoral person? Or in the same sense as an amoral rock? In a Western context, those are effectively two different definitions of amoral. The evidence for this claim is that an amoral agent is repugnant to us, whereas the idea of an amoral rock just makes us shrug our shoulders. Effectively, only agents are amoral when viewed through the Western lens. Some might consider the universe to have agency, but attributing agency to the universe is superstitious in one form or another.
The same construct applies to Buddhism from a Western point of view. The phrase "I don't care" can sounds callous to a Westerner, because in Western culture, you are supposed to care -- indifference has a nearly inescapable negative connotation. But in the West, "I don't care" can also mean "I'm fine with whatever you want" or "I'm fine with whatever happens" -- a serene, unselfish, generous detachment.
So it seems shaky to consider Eastern detachment and Western nihilism as two different words for the same thing, especially when talking about altruism. A monk can teach an initiate how to attain enlightenment without being invested in the outcome -- nihilism connotes rejection, detachment connotes abstaining, of not even approaching the question of investment or rejection.
Even in Western culture, we sometimes do things because they are good things to do, without giving a thought to the outcome. "Good" in this context doesn't necessarily mean assigning moral value, it can mean "that's the choice I make" without the need to explain it. This relates to Kant's idea that (very roughly phrased) since no person is more important than another, that all should be treated equally. This can be more of a logical, reasoned or even mathematical conclusion than one of altruism.
