They can, but there are limits.
Mine are trained to go on concrete/hard surfaces as I find it much easier to pick up and squoosh from my wheelchair vs trying to drag a turd out of long grass with a poopickstick. Our verges are almost exclusively long grass as our council is one of those 'lets not mow it let the wild flowers grow' jobs, so it is only cut back twice a year.
I can't ALSO train them not to go on concrete/tarmac (it's what I have in my back yard), and they can't really differentiate between my concrete/tarmac and someone elses).
On the whole mine shit before they go out, but exercise does tend to prompt further shitting. I ensure their diet is such that poos are easy to pick up and carry a sports bottle of water for squooshing with if necessary. I think that is sufficient, the pavement is for walking on, you're not meant to be lying on it or licking it.
They're also not allowed to wee up gates/cars/peoples property, as I think thats disgusting - certain street furniture that is made from anti corrosive stuff I do permit as it is an instinctive need, to sniff the peemail and scent mark, and no ones stopping the foxes, cats, badgers and munties from doing it, all of which is interesting scent for my dog to follow/investigate.