The hunters radioed for help shortly after they were dropped off by helicopter at dusk in the mountainous woods of Norbotten, claiming to be under threat from some of the roughly 900 brown known to lurk in the region.
But as the evening light was dwindling fast, the helicopter pilot explained he wouldn't be able to fly back to rescue the hunters until the next day.
"I was on another assignment and we don't fly in the dark so they had to sit in a little shelter. It's like a little box," pilot Johan Nordlund told the paper.
So the hunters spent the night cowering in their shelter, waiting for the bears to strike.
But when they peered out from their shelter in the morning, they found themselves face to face, not with a pack of ravenous bears, but with three harmless cows that had apparently lost their way.
"I asked, 'Are you guys drunk or what?'" Nordlund, the helicopter pilot, told Aftonbladet, adding that he thought the hunters were joking when they radioed back to call off the rescue operation.
As the nearest Swedish cattle farm is more than 100 kilometres away, it's likely the wayward cows hail from Norway, according to the paper.
Nordlund, who has seen the bovines on flights in the area in the ensuing days, last saw the visiting cows heading into a nearby national park.
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"Maybe that's what they came over to see," he quipped.
He warned that the cows' owner must be found and the livestock returned before winter's chill takes hold in the region.
"They'll die when winter comes," he told Aftonbladet.