KC Dad,
I probably didn't explain it as well as others might. The big difference in football is there's no bag that has to be touched. I'm surely no expert on passing routes, but if the outside foot is "always" used to turn on, there must be a good reason. My question would be... if your running full speed and you make a left turn off your outside foot... where does your inside foot go on the very next stride?
In running the bases... If you at full speed touch the base with your right foot... your left foot in it's next stride almost has to go beyond your body (in it's path to the next base). This would be much easier to explain with drawings.
If your inside foot touches the bag... your next stride is right foot outside your body... where it should be. You will make this turn faster with better balance and gain better footing and leverage in using the bag to push off of. It is much easier to create a shorter/straighter/faster line to the next base.
My suggestion is to have your runners do it both ways and watch. I think it will become fairly obvious after awhile. Of course, there is more to it than simply using your inside foot. There is technique involved in doing it properly.
When rounding the bases, the most critical distance is between the base your trying to reach and the base right before it. In other words if you read sure double possible triple you will set this up for as straight as possible line from 2B to 3B because there will be no play at 2B. Same for being at 1B when the hitter hits one in the gap, you'll want 3B to H to be as straight a line as possible, because there won't be a play at 3B. Same as getting a base hit to left field, you start rounding because there won't be a play at 1B. It's on these final turns that using the inside foot is most beneficial.
This is one of those things that is hard to describe in words (I guess) and very simple to describe on the field. Sorry, if it's hard to understand.