The idea is that either leaf wetness allows the fungus to infect the plant (which is typical for most plant fungal diseases) and/or rain splashes spores from one leaf to another. Rain and overhead irrigation can obviously do this, but high humidity can also cause leaf wetness. That's why good plant spacing is important so that the leaves can dry quickly with better air circulation. Also drip irrigation is better than sprinklers because it keeps the leaves drier, and not overhead irrigating late in the day or at night is best because then the leaves dry quicker.
There are two links at the bottom of the AHS page I gave above, one is an overview of the disease and the second one is a link that shows which fungicides tested most effective.
The leaf streak fungus is reported also to need a wound such as from weather (e.g. hail) or insects before it can enter the plant so that's something you might also want to look at. If you don't get much natural rainfall is there a chance the plants are suffering from drought, or do you water them?
