Niall -
Tom Doak is better positioned to give an answer. But in his absence, I'll take a whack at your question.
Minimalism, as I understand it, is not primarily about appearances. It's main goal is not to build golf courses to appear 'natural' (however you want to define that.)
It's about actually moving as little dirt as possible.
That is the main goal because on good sites the natural contours in fairways will almost always be better than contouring built from the seat of a bulldozer. Tom has noted in the past that small, subtle movements are a defining feature of many of the best Golden Age courses. It is part of why they have the reputations they enjoy. Their fw surfaces tend to be less predictable, more severe and more interesting than anything that might be planned and 'built'. It's one of the payoffs for the lack of large earth-moving equipment in the GA - you get a better, less predictable, more challenging kind of golf.
(The other benefits or minimalism of the sort I have in mind is that you get faster grow-ins and, later, healthier vegetation because it was already established at the site. Another topic, perhaps.)
The natural look of such courses is all fine, but that is secondary to building a golf course that enhances the quality of the game played on it. The way courses like TOC or NB or Carnoustie (or pick your GA favorite) do. Which ought to be the point of good golf course architecture, no?
I said "good sites" above. There are flat sites where more construction is needed (think the Rawls Course or TPC Sawgrass). Given the additional earth-moving needed, I'd guess that the goal of achieving a 'natural' look might have more prominence in the scheme of things at those sites.
Likewise the construction of greens and their surrounds. They require more earth-moving, but earth-moving can be minimized and naturally existing, subtle land forms utilized. Again, with the goal of making for a more interesting brand of golf and not primarily to achieve a certain 'look'.
Thus my own take on minimalism is that it is not about building 'natural looking' courses per se. Lots of people have made and still make that a goal. I think that goal misses the mark. Most interesting about 'minimalism' is that it seeks to move less dirt because moving less dirt (again, on good sites) offers better golf. If the resulting course happens to appear 'natural', so much the better. Given you are moving less dirt, it probably will. But even if it doesn't, it is not a cardinal sin.
I hope Tom will chime in on this. He will express his own views better than I possibly can. The above is meant to respond to your question as to whether 'minimalism' can be reduced to a simple concern with 'natural looking' features.
Bob