In a viral video, the man walks up to the family as they emerge from a field to cross the road. After the young bears scurry behind a parked car to follow their mother, the man heads to the front of the car to meet them on the other side.
The displeased mother then appears to charge at the man before backing down at the last second.
"I honestly thought we were going to sit there and just watch him get mauled," Paige Marple, who shot the video, told WBIR.
After the video went viral, the park released a statement urging visitors to "act responsibly" around bears.
"Bears should never be fed or approached," the statement read, according to WBIR. "We work hard to keep bears wild in a space shared with 11.4 million people. We need each visitor to do their part by always staying at least 50 yards back from bears and properly disposing of food waste – for their safety and that of the bears."
Anyone who gets closer than 50 yards to one of the bears could be arrested or fined, officials said.
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