Some thoughts on OW training, at least for PADI:
In the classroom, if we just follow the course plan, we spend a lot of time teaching how to measure dives for purposes of avoiding DCS, and a relatively small time talking about about lung overexpansion injuries. There is not much time spent on gas planning or buoyancy at all, except for the need for the latter. Consequently, the wise instructor will add value to the class by talking about these things in more detail.
In the pool, there is nothing about DCS or gas planning, and a little on proper ascents to avoid injury. In the latter case, there is actually a lot of it permeating the class in the background, since the goal of much of the instruction is to teach comfort in the water and avoid the panicked bolt to the surface.
Buoyancy is the wild card.
If you look at the standards carefully, students are supposed to learn to swim with proper buoyancy, but I would argue that it is not typically done effectively. Students have to perform a number of skills, they are given two buoyancy specific skills, and they are supposed to do free swimming to learn to be comfortable in the water. The last part of that sentence is not well defined. If they do the skills non-buoyancy skills negatively buoyant on their knees and then do a minimum of free swimming, they will leave the pool sessions with little buoyancy skill. If they do the skills while neutrally buoyant and if free swimming time is stressed, they will come out with pretty good buoyancy skills.
The buoyancy part is thus up to how the instructor chooses to teach the class.
