Generally they try to drill underneath your driveway, and trench in-between driveways on adjacent properties. They drilled underneath my driveway earlier this week, I am currently waiting on the trenching team.
They trench and install the grey box on your property edge at around the same time (this is were your preferred fiber provider will attach their CPE), if the grey box can be mounted to some publicly accessible wall/vibracrete. If not (for example if you have a palisade fence) they leave the grey box in the "mini" man hole/junction box on your property edge (usually shared between two properties) for your preferred fiber provider to install at a later date, as they are not allowed to go onto your private property without your consent.
This is not always the case however, especially for the part between your home and the junction box, that part is always trenched, unless you have that section done privately.
TL: DR - They try not to dig up your driveway unnecessary for the main Fiber Lines. Yes, they are allowed to dig it up, as your private property ends at your fence border and does not extent to the public "sidewalk".
Also, if you are not being a dick about it, they tend to be rather accommodating, just talk to the foreman on site.
#P.S. - Please don't spoil the fiber experience for all of the people further down the street from yourself. And brace yourself for a power/water cut or two as they will more than likely hit unexpected/undocumented buried infrastructure...
