Here is the only brockage I have. It is counterfeit, British made, British half penny. This was far more affordable than a U.S. coin brockage. Here a normal example of the counterfeit. I am going to assume that the obverse die is at the bottom on the press. This is the way the press was usually set up because the bottom die lasts longer the top or striker die. Since it often takes more effort to make an obverse die, the the coiners would prefer for it to last longer. For the brockage, the previous coin stuck to the upper die. When a blank is inserted and the coin stuck, the previous coin's obverse struck the reverse of the planchet, therefore creating the mirror image. The obverse of the brockage would be normal.
It's really hard with coins, because we're conditioned to expect the design to be in relief (raised). In that photo, look at the top of the coin. See the shadow cast by the plastic insert? That shows that the light is coming down from the top of the slab, with the coin below the level of the insert. Similarly, all the coin's design elements are brighter at the bottom, shadowed at the top, indicating that they too are lower than the fields -- but you've got to mentally focus to see it that way.
This in fact was true. The anvil (bottom) die vs the hammer (top or striker) die was typically oriented the way you say, John. I'm not 100% sure this is always true today.