Since the actual coat is on display at Ford's Theater, then it should be obvious is a swatch was taken from said coat. It would seem that experts could determine authenticity of the swatch being material coming from the 1865 era.
"How do we know what's genuine, a fairy tale, a wish or fraudulent?" said memorabilia broker Daniel Weinberg in Chicago. "It needs more than someone saying it appears the cloth may be similar to what Lincoln wore."
In a similar regards, there was a nice (and highly critical) article in Macleans (Canadian news weekly) in regards to the (in)famous James Ossuary that supposedly provided concrete existance of Jesus. The article nicely descibes how the Royal Ontario Museum (in someone's foolishness) was taken for a ride on this fraud, and what the shaddy Israeli art dealer went through to pull it off. . .
Here's a bite:
When workers at the loading dock unlocked the doors of the Brinks truck on the morning of Oct. 31, 2002, Dan Rahimi, then the ROM's director of collections, blanched. The priceless James ossuary, trumpeted on the world's front pages only 10 days before as the first historical evidence of the existence of Jesus Christ, was packed in a cardboard box like a discount-store toaster oven. The normal protocol for shipping an antiquity is to put it in a foam-lined wood or metal crate, placed inside yet another sturdy foam-lined crate. "I looked at it and said 'Oh, f**k!' " Rahimi recalls. "I mean, it was so bizarre."