That's actually a different hypothesis than the one presented by santa above.
That being said, the data from experiment 1 above strongly implies that this is not the case.
If you look through the full season by season data from experiment 1, here are the relevant points of observation to note:
First, we can measure the amount of demonstration watching a recruit has done pretty directly by observing their studying skill.
Second, we can get a good idea of the amount of sparring a student has done by observing his discipline skill. I'm not positive, but I believe that no discipline is gained from observing a demonstration. Regardless, we can observe that the amount of discipline gained from individual combat drills, combined with any potential gains from watching demonstrations, is a mere trickle. During the first season, most recruits in squad B gained 2 levels in discipline. During the third season, they mostly gained between 2 and 3 levels in discipline and those levels had much steeper exp requirements to boot. In essence, while a soldier could probably attain level 20 discipline from individual combat drills alone (if he didn't die of old age first...), he would be rapidly outpaced by another soldier that was sparring, even just a few months out of the year.
Having established some rulers, we can see that each soldier in squad B spent almost as much time watching demonstrations as the soldiers in squad A did. Squad B simply started sparring sooner and pretty much just maintained that initial lead.
My working hypothesis at the moment is this:
Each soldier attempts to balance his training schedule between two tasks at a fixed ratio: Sparring and Demonstrations. A recruit will do individual combat drills in two specific situations. First, if he is scheduled to spar, and cannot due to fatigue, lack of partners, etc. Second, if he is scheduled to participate in a demonstration but cannot, due to lack of demonstrable skills, lack of partners, etc. We have no real control over how this internal schedule is laid out, but it is possible that some factor may effect it. For example, perhaps a dwarf that likes to brawl will have a higher ratio of sparring to demonstration.
The skills demonstrated seem to have less to do with the gap between teacher and student, and more to do with an internal priority arrangement based on a minimum level of competence. For example, we can see pretty clearly that squad A was heavily focused on dodging and, to a lesser degree, striking first. What internal mechanism determines the order of this priority system, I don't know. All I can say is that if it was based purely on the gap between skill levels, the skill gains from demonstrations in squad A would have been much more uniformly distributed, as the teacher was level 20 in nearly everything.
The reason that squad B gained an initial sparring lead is very simple. They had no dodging or striking skills to demonstrate. The only skills they where gaining from individual combat drills where fighter and discipline, which led to demonstrations between students on fighting, simply because it was the only skill they could demonstrate. This means they hit level 3 fighter sooner.
Similarly, Squad A gained an initial studying lead and simply maintained it for the exact same reason. Their teacher did have a dodging and striking skills to demonstrate. Since the demonstration portion of their schedule was taken up by these lessons, they did not gain fighter as quickly.