"At a guess and knowing that they were not stupid. I would say the step preceading the Three Step might not become a Three Step."
Of course not. But if it does become the step preceding a three step, this first heel lead is Heel (only) with no rise, while the second heel lead - the one document in the three step itself, is Heel-toe, with rise.
Or look at a chasse in waltz or quickstep. Last step is given Heel (only), outside partner in CBMP. Quite often this would also become the first step of a natural turn, in which case the fact that it's the first step of a natural turn with rise changes the footwork to HT, while the fact that it's also the last step of the chasse keeps the action outside partner in CBMP. On the other hand, we could dance a double reverse spin or a quick open reverse instead. In those cases, the last step of the chasse would be only the last step of the chasse and performed as written - Heel (only). It would then be followed by the first step of the DRS or QOR, danced HT.
So you see, there are heel leads that don't rise, are coded (Heel) only, and see the heel come up late - and would ordinarily be followed by a second heel lead. And then there are the more common heel leads which are coded HT, do rise in at least some respects, and see the heel come up early.
And finally, there's what's documented in the book for the walking EXERCISE, which is somewhat in between, with the heel rising exactly as the feet pass.