“It’s not a reasonable excuse,” he told ABC Radio.
Mr Fuller noted the learner driver incident occurred interstate “but nevertheless I’m sure there is examples in NSW”.
He said carve-outs existed for things such as travelling to work, get food or medical assistance, or to exercise.
“But if we carve out every activity then there’s no point having the isolation,” Mr Fuller said.
“If you don’t really need to do it, then stay home and stay safe.
“States and territories around the world who haven’t taken this seriously have been punished through lots of deaths.”
He defended policing of the state’s social distancing and isolation requirements, saying that as of Monday there had been just 21 tickets issued.
Under COVID-19 measures, police officers have the power to hand out fines of $1000 to individuals and $5000 to businesses that breach public health orders or ministerial directions.
Mr Fuller said there had been a lot of cautions and he’d asked for a “high degree of police using their powers of discretion”.
“I know there’s footage from day one in NSW where police were driving through a park, and that footage continues to haunt me, but we haven’t been applying the law that way since then,” he said.
Some tickets issued on Monday related to a couple of Sydney brothels, a woman who refused to leave a casino and a man accused of a church break-and-enter, Mr Fuller said.
On Tuesday, two police officers were among those to be issued $1000 infringement notices after breaching public health orders while off duty over the weekend.
Police say one, a 27-year-old senior constable, looked intoxicated when officers saw her being assisted by a man in Sydney’s CBD on Saturday night.
She was taken to St Vincent’s Hospital for treatment before being released the following morning.
Police established that she and the 31-year-old man had been at a social gathering a nearby apartment, along with a 27-year-old male senior constable and two other women. All five have been fined.