Close, but not quite right.
The Right-of-way is defined by the subdivision plan or plot of lots for a developement. Absent such a plan or plot, it's defined (more or less) by the monumented front corners of properties.
The cartway or travelled way (legal terms for the paved or otherwise improved portion of the Right-of-way) may lie anywhere within the Right-of-way. Pavers often cheat on corners, cutting them inside of the centerline of the Right-of-way.
You can't just split the curbs or the pavement to determine the extents of the Right-of-way unless there's no existing monuments and splitting them agrees with lines of usage (though some shoddy hacks do it routinely). I do this mundane stuff for a living.
Regarding this ordinance: you own everything, except public utilities, from your property lines to the sun. If it hangs over your property line, you can cut it off. That's a general rule--however, your actual mileage in communist states like California, Vermont, Connecticut and New York may vary.
LOL
I bet this 'right of way" is included in the taxes paid each year!
Up here they dump snow in your front yard, which can get pretty deep - and don't even think about cleaning the drive and putting the snow in the street...
In Vermont, where we live now, right of way is currently measured in feet, but was originally measured in rods. You had three-rod roads and five-rod roads.
In our current case, the town controls from the center of the road 25 feet on each side, which is about 10 feet into the grass.
We have ornamental trees and flowers that encroach on that area here and there, which is fine as long as they don't obstruct the view. But our picket fence has to be 25 feet from the road center, and we need permission to change anything substantially in that area. But the Town Clerk is a reasonable person, willing to honor any reasonable request.
And, yes, the Scarsdale politician is wrong if he thinks you can't cut any parts of trees that hang over your property. And he's stupid if he won't allow residents to reasonably prune trees and remove dead branches, because that saves the town maintenance crews time and money.
If a tree gets rotten and threatens to fall on your house from town property, then you get into a debate with the town, and hope they will be rational. In our town they would be rational. In Scarsdale, you might have to write the local paper and threaten to sue them. Incidentally, we once lived in Scarsdale.