Woods, whose solution to the traffic is to stay on his $20m super yacht close to the course, believes the mayhem could make somebody miss their tee time.
Fox's coach Marcus Wheelhouse also takes a cautious tone, saying it makes it difficult to prepare properly.
"It's pretty crazy, it has taken us three hours for what would normally take an hour. You need something that Elon Musk [SpaceX founder] is inventing ... or a helicopter," he told D'Arcy Waldegrave on Radio Sport.
"There's so many people coming to the event and there's only one road in and one road out. You're going to have to spend a bit of time sitting around at the clubhouse so you're actually sure that you're going to make it.
"You just have to prepare the best you can."
Despite the brief scare, Fox got through his practice round, and feels more at home in what will be his fourth major championship.
"Everything just feels a bit more comfortable, [but] that doesn't mean I'm going to play well or anything like that," Fox said.
"But it's nice just to be able to enjoy the experience a little bit more rather than my first couple where the nerves are there and everything feels like it's going so fast.
"This week I'm just here to play another golf tournament."
Fox comes into the tournament in decent form, having made the cut in his last four events, including claiming a tie for eighth at the Italian Open earlier this month. He is joined in the field by fellow Kiwi Tim Wilkinson, who is playing in his second major following his tie for 61st at the 2016 US Open.
Fox tees off at 4.30am on Friday, while Wilkinson gets underway at 12.46am.
