Yes, urine can kill grass. There are actual products on the market that are sold to give to dogs to change the composition of their urine to make it less likely to kill off patches of grass.
I don't recommend using these products....
I do not think a bit of dog urine could really kill a bush or a tree. :)
Many people have dogs and leash walk them at the curb or on the sidewalk as per city ordinance.
What about things like hardy landscaping plants?
Although the urine deposited there could cause some brown spots on the grass...it should not really affect the trees and bushes.
As I mentioned above, I don't believe the urine will do much to hardy plants and trees.
It might affect little tiny flowers, like impatiens...
I agree with your decision not to walk your dog in that direction anymore.
If you have further questions concerning this matter, please just let me know as I would be happy to address them for you.
Thanks...What an interesting group of people in a very dog-oriented neighborhood.