This is correct. The Shroud could be proven to be a hoax, but could never be proven to be the burial cloth of Christ. However, if it can't be proven to be a hoax, which it can't until the source of the image can be determined without doubt, then which is more likely, genuine or hoax? The longer it remains a mystery, the more likely its authenticity, in my opinion.
What changed all of this was the advent of photography. An Italian photographer named Secondo Pia received permission to photograph the Shroud during one of its rare public displays, and while he was developing the film he produced a negative that had far more detail than the original image (the image you see at the top of this thread is the negative, not the original).
The implication of this was immediately clear to Pia: The "negative" he was looking at was actually the real image, and the "original" image on the Shroud was actually the negative -- which meant that whatever process was used to produce that image was identical to a photographic process that the world had only discovered recently!