It is true that using less water will reduce the chance of "glycerin" rivers. Overheating and uneven saponification aren't the reasons why rivers form.
Soap is made of many different kinds of soap molecules. Oleic, stearic, and palmitic soap molecules are usually the main types found in many soaps, although the composition of any given soap depends on the fats used to make it. Some of theses soap molecules crystallize (solidify) at higher temperatures and others solidify at lower temperatures. This progressive crystallization process
always happens in soap, but sometimes we humans see the results of crystallization as obvious crackling or rivers, and sometimes the crystals aren't visible.
When a batch of soap gels (turns into a soft semi-liquid paste) and then cools, the palmitic and stearic soap molecules crystallize first. The liquid oleic soap molecules flow out and away from the solid bits of stearic and palmitic soap.
If this process of crystallization and separation is allowed to happen slowly enough, the opaque parts and translucent parts of the soap become large enough so they are visible to the naked eye as crackles and rivers. If the process happens faster, the different crystals remain very small and pretty much invisible to our eyes.
The process of crystallization and separation happens often in many areas of life.
Here's an example -- Have you ever put a can of soda pop in the freezer and forgot about it? If you take a close look at the frozen soda before you clean up the mess, you'll see translucent ice crystals floating in a thick syrup of dark, sweet soda syrup. If you could cool the soda syrup even colder, the syrup would also eventually freeze. The result would be a mixture of clear ice crystals surrounded by frozen syrup. This is the soda pop version of "glycerin rivers" in soap.
Another example is making fudge or taffy. If you do not stir fudge long enough or knead taffy properly, the finished candy will have large gritty sugar crystals in it. If you do things right, the sugar crystals remain tiny and the candy stays smooth, pliable, and silky.
More:
Soapy Stuff: Crackling, streaking, and mottling