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I think I'm communicating a little poorly. So start with atomic level physics- it's characterized by energy scales of 13.6 eV or so. Making measurements at that scale will tell you a lot about atomic level physics, but it won't tell you anything about lower level physics- there is an infinite number of of lower level physics theories that will be compatible with your atomic theory (which is why you don't need the mass of the top quark to calculate the hydrogen energy levels- conversely you can't find the mass of the top quark by measuring those levels).
So you build a more powerful microscope, now you can get to 200*10^6 eV. Now you'll start creating all sorts of subatomic particles and you can build QCD up as a theory (which is one of the infinitely many theories compatible with atomic theory). But you can't infer anything about the physics that might live at even lower levels.
So you build a yet more powerful microscope, now you can get 10^14 eV, and you start to see the second generation of quarks,etc.
At every new level you get to, there might be yet more physics below that length scale. The fundamental length scale is maybe the planck scale, and we are still 13 orders of magnitude above that.
Edit: this author is sort of a dick overall, but this was a good piece on the renormalization group- http://su3su2u1.tumblr.com/post/123586152663/renormalization-group-and-deep-learning-part-1
I think I'm the one communicating poorly since it seems I understood your first explanation, thanks for making it sure anyways and thanks for the link!
When I was wondering about successful predictions in particle physics, I was in particular thinking about Higgs boson. We needed to build a massive "microscope" to detect it, yet could predict its existence four decades ago with much lower energy scale equipment, right?
The existence of the Higg's is one of the rare bits of physics that doesn't average out under renormalization.
The reason is that the Higgs is deeply related to the overall symmetry of the whole standard model- you start with a symmetry group SU(2)xU(1) and then the Higgs messes with the symmetry so you end up with just U(1) symmetry. What the theory predicts is relationships between the Higgs, the W and Z boson, but not the absolute scale. The general rule is RG flow respects symmetries, but other stuff gets washed out.
This is why the prediction was actually "at least 1 scalar particle that interacts with W and Z bosons". But there are lots of models consistent with this- it could have been a composite particle made of new quark-like-things (technicolor models), there could be multiple Higgs (2 in SUSY, dozens in some grand unified models),etc. So it's sort of an existence proof with no details.