You are right, of course, that a spider's web -- or any other object -- is not simply a construct of the mind (Unless we get completely Socratic in our thinking). However, to define a limit to any physical object is indeed a mental exercise -- the closer you look, the more you see there is no defining edge (although to be fair, I concede that the painterly invention of "lost edges" refers not to atomic theory but to parallax etc. -- more on such illusions below).
Although this is usually a distinction without a difference -- human beings have such powers of delineation and definition to make sense of the world around them -- there are concrete consequences. For example, in a life-drawing class, I doubt that any two artists will portray the same model with exactly the same set of lines (It would hardly be art if they did).
The subjects we objective artists portray are real; but the lines we draw are subjective, depending on such physical factors as our distance to the subject, our angle of view, the detail viewable in the available lighting, etc...
http://www.optillusions.com/
...but equally importantly, what we choose to portray or not portray as artists with our lines or colors says a lot about ourselves and our subjects -- which I believe is at the heart of what you've been getting at.
Beyond technical proficiency, of laying out lines in geometric accordance with the forms observed, are we to draw and/or paint our subjects "warts and all" or in the most flattering view?
Like I said, I admire it all!