No, it doesn't mean "no." I use pretty good brass, RWS or Lapua or Norma. I did my little test, and found no direct correlation between case weight variance and velocity. With the big cases I shoot, a 3-grain difference in weigh showed no correlation.
As far as velocity variance from all possible causes, it is hard to get a low enough variance not to show up at long range as vertical stringing, which is why we have to tune the load. The first level of "tuning" is for accuracy -- what kind of powder, what bullets, etc. The second, and what we are almost always talking about on this forum, is "tuning out, the vertical." When you get this tune, it doesn't really matter what the velocity spread, as long as it is reasonable.
For example, I remember Steve Shelp doing a lot of testing, and he found that the most accurate powder he could come up with for his .338 Yogi didn't give as low a velocity spread as another powder. With the higher ES/SC of the more accurate powder, he had a little more work in load development, but when done, he a very accurate combination.