Here are few pics of my young trees that I am training then to grow horizontally and rounded.

Navid.

I read somewhere ( I think) about  horizontal growth encouraging more fruit- is this the basis?

Horizontal branching has been used for climbing roses and other flowering shrubs to increase flower production and fig is an inverted flower so the technique should work to increase fig production.

You are correct. But, to force the horizontal branches to produce more fruits you need have a good amount of branches on those trunks or branches. To do so, I cut the main leader and pinch the leaves that are facing upward. Doing so forces the tree to send out new branches from those node where the leaves were taken off.
Usually takes a week or so to see the a small branch emerging out. After a month or so when the new branch on the top is 5-10 inches long, I then pinch off the lower leaves and proceed with the same method.

In pics below you see the new branches emerging from the node where the leaf were pinched off.

Or if you don't want to grow horizontally and would like to have a tree that goes vertically up. To increase your fruit production, again you must have a good amount of branches. To do so, I cut the main leader on tree that is 4-5 feet tall or (how tall that you would like it to be), then I pinch off all the leaves only leaving 3-4 on a 4 feet tall tree. Then you will have a tree shaped vertically with many branches, that will increase the number of figs/fruits your tree produces.

This method will be more like a Espaliered form than the previous method.