The hair was subjected to genetic testing at the FBI crime lab in Quantico, Va.
CBS News Correspondent Kelly Cobiella, who's in Aruba, says the results gave Holloway's family some reason for optimism.
They say it's a relief, and, with Natalee missing two months, they want investigators to go back to Week One.
"I just want to go back to the beginning, because there were a lot of clues right at the beginning of this," says Holloway's stepfather, George "Jug" Twitty, husband of her mother, Beth Holloway Twitty.
The family is convinced all the answers to Natalee's disappearance are within five miles of the hotel where she was staying, and finding duct tape on the other side of the island simply didn't fit.
"We never really felt like that was something that we were sure about," Jug Twitty says. "We've been through the ups and down of so many different things like that."
But, adds Cobiella, they do sense there's something at the bottom of a floodwater basin. After more than two days of draining, crews think they'll have it dry enough to search for evidence Friday.
Tim Miller, who heads the Texas search firm EquuSearch, says, "I don't believe they're really looking for Natalee's body in the water. I think it's more an evidence search. They're trying to find some evidence."
His teams scanned the sand dunes in a remote national park Thursday, using radar equipment to "see" underground. They were led there on a tip a month ago, but wanted to do a more thorough search.
They plan to do the same at a landfill today, acting on yet another tip.
Yet, says Cobiella, it's a rumor that's giving Natalee's family the most hope: a rumor that the high school grad was kidnapped, and is alive somewhere, and that thebeing offered in the case will help get her back.
"I mean," says Jug Twitty, "wouldn't that be unbelievable if it came about because of that? I mean, gosh, yes, we hope that very much."
The family doesn't think the abduction angle has been pursued thoroughly enough by authorities in Aruba, Cobiella says.
There's also a court ruling expected Friday on whether authorities had the right to take DNA from three suspects in the case.
Even if that evidence is thrown out, Cobiella notes, it would amount to more of a procedural delay than anything, because prosecutors could, and likely would, ask for more samples.