Both. The ideas we bring with us and the ideas that develop over years of training. We all have both these things, and we all let both these things affect the way we train.
There is a big difference. I just don't think I have the authority to decide which of these two is "right" or which amounts to "true understanding". I know which one is more interesting to me and more relevant to my life, but to claim to know any more than that is to speak for an art that never named me its spokesman.
It strikes me that you're talking about two different things here: what budo is, and why someone would do it. To me, the question that began the thread implies the former (it concerns what budo is) and does not at all address the latter.