The reason for head-to-head coverage is because the amount of water reaching the ground varies based on distance from the head.
While this is not a quote of any specific system, here's a represenative example.
Place several rain guage in a row spaced 1 foot apart starting 1' from a lone sprinkler head (i.e. pretent that all other heads have not been installed yet). Let the system run for an hour and come back and check the water level in each guage. The first one has 2" of water. The second has 1.75". The third one has 1.6". etc, etc until the last one has 0.5". So if you install another head at the last rain guage (and turn off the original head) turn the water on again and you get the same results (execpt backwards, the last one that is now closest to the head is the one with 2"). So now if you try it a third time with both heads on, the first and the last guage will show 2.5". All the others in between will also be close to 2.5" (with perhaps as little as 10% difference, where as with one head, the level varied by 300%).
Keep in mind this is a totally made up example (for all I know, its the gauge farthest from the head that got 2" and the closest got only 0.5). But it still shows how by having all points between the heads getting water from both heads, the 2nd head makes up for the short commings of the first.
I think I've read the general suggestion is that if you don't want 100% overlap like the designers did it, it's a general rule of thumb that you're ok as long as you have at least 80% overlap. That means if the system was designed with 100% overlap on 40 foot head spacing, you should not increase the head beyond another 10 feet (i.e. 50 foot head spacing).
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