You're right. John mentions a face cloth too.
If people need something that tangible to believe, and it shakes their faith if it turns out to be a fake, they didn’t have much faith to begin with. I find it interesting (I would love to know how it was made) but it seems unlikely that it’s really the shroud Jesus was buried in. And when I first heard of it, I wanted to believe it was real (because I thought it would be cool to know what He looked like).