Of course this is dependent on location, there is no shortage of 'urban' areas where there is no where near the amount of bugs available, while greens can still be readily available in copious amounts... The way I look at it ounce for ounce I'll bet most free range;backyard' birds have access to much more low protein then high protein options in the urban back yard, but of course that varies by location, there are obviously areas where the opposite will hold true... Consider this if we convert to a dry standard a bug like a meal worm has 53% protein, while random dried greens probably have a dry protein content of give or take 12%, that means to give or take exceed 25% protein the chickens grazing diet would have to be about 1/3 bugs, and I doubt that is likely in many urban environments, especially in neighborhoods where it's trendy to treat the lawns, trees and what not for bugs and weeds...
Sure too much protein or anything can cause problems but even a 30% protein diet is far from that danger threshold... Also I have to wonder how one would go about feeding a level of protein at a level that actually causes harm due to protein content, basically you would have to feed an all meat diet or highly refined plant meal diet... I suspect the real cause of issues with a 'higher' protein diet is that lack of it being a balanced diet overall, not necessarily the extra protein... No doubt eating only meal worms would not be good for chickens but I argue it's not due to excess protein but instead due to a lack of other necessary nutrients...
One has to also consider the 'quality' of the protein, the reality is a balanced amino acid protein content of 16% can actually be far superior to an unbalanced higher protein feed...
If one looks at this article for example
http://japr.oxfordjournals.org/content/18/3/477.full you can see that before synthetic amino acids were developed that to get the proper amounts of amino acids from soy and corn protein the feed had to be about 35.6% protein... This protein level was necessary due to the fact the feed was not nutritionally balanced...
Have you looked at a non-medicated 'starter/grower' there is essentially no significant difference between an 'all flock' and non-medicated starter...