Do successful french macarons really need precise weight measurements?
I can tell you that yes, every part of the process, including precise measurement, has really low error tolerance. Do something a bit wrong, and you end up with an edible cookie, which does not resemble a macaron in shape or texture. 

My explanation for the different ratios you found is: the really important thing about the ratio is the final moisture content of the batter. Different recipes exist, because there are different ways to reach the same final batter moisture. 


both sugar and almonds bind moisture from the egg whites. So it isn't enough to look only at the almond:eggwhite ratio. The recipes with more almonds probably use less sugar, if the process is similar. 
the process itself matters a lot. Making an Italian, French or Swiss meringue will have an influence on the amount of liquid available for the almonds to absorb. 
almond flour does not have a standard moisture content. If a chef has his almonds cracked daily and processed into flour, they will absorb much less water than if he buys a pack of almond flour at the supermarket. 
aged eggwhites will behave slightly differently than unaged, some recipes will be written for aged eggwhites and other for fresh ones. 
finally, not every recipe out there is a good one. It's very possible that a few recipes from your sample will never produce a good macaron. 


You are, of course, welcome to try it without the precision. Especially after you have mastered them, you can play around and see if a different recipe gives you a slighlty different texture which you prefer. But if you already have a recipe which is supposed to work, I'd avoid changing anything about it.