Yep, it sounds a lot like something a Muslim would say. Christianity has NEVER taught that a likeness of our Lord was idolatry.
The Shroud of Turin is either the burial shroud of our Lord or it isn’t.
If it IS NOT, then why hasn’t anyone been able to explain how a medieval forger could have made it? For that matter, why are modern scientist unable to make a perfect reproduction TODAY? It seems that those should be very simple questions to answer.
However, if it IS the burial shroud of our Lord that would mean that He WANTED His image to be shown on the shroud. If He WANTED it there, it means He WANTED us to see it and that would mean that He produced what some denounce as an idol.
The Church has, of course, been reticent to pronounce one way or another on this, citing gaps in the shroud's provenance. Which is the proper course of action at present. Nevertheless, it's interesting not only from a religious, but from a scientific point of view.
When I was a physics undergrad at the U. of Rochester, the chairman of the department was Harry Gove. He was a shameless publicity hound, but he was (probably) the first to propose a method of carbon dating using very small sample sizes, and analyzed by means of particle accelerators, in this case Rochester's "Emperor" tandem Van de Graff, used for studies of atomic nuclei. Naturally, the Shroud would have been a perfect candidate for this kind of testing, since one would not wish to sacrifice any more of it than absolutely necessary. The upshot is that Rochester wasn't one of the groups chosen, but those two that were used a similar methodology to Gove's.
Although those results indicated a medieval date for the cloth, there is still controversy over whether or not the sample was contaminated by carbon from the fire the Shroud had been through, or whether the sample actually came from a patch used to repair the cloth, or if a biotic plaque on the surface of the material skewed the results. The only way to resolve this would be with another round of testing, monitored to everyone's satisfaction.
From my point of view, though, the scientifically interesting question is how the image was actually formed. As you've pointed out, no one has really been able to answer that adequately in purely material terms, nor have they been able to reproduce the process. It's decidedly not a simple question to answer, as it looks like the obvious explanations, e.g., it's a painting, it's some primative quasi-photographic process, etc., have been pretty much discounted.
I have no knowledge apart from what I've read in the public arena, but it strikes me that the tonal distribution of the image resembles that of an X-ray. That is to say, it's what one might expect if the cloth responded to incident radiation according to Beer's Law. (In fact, X-rays were first discovered by observing the exposure of photographic film in their vacinity.) The Beer's Law distribution suggests a "(super-)natural" process of image formation, rather than a man-made one, like a painting, though it doesn't necessarily mean the incident radiation was in the X range of wavelengths. Another interesting aspect of the image is that the presumed incident radiation was normal (i.e., perpendicular) to the surface of the cloth.
Finally, the objection is sometimes raised that even if the cloth could be traced to the first century, it's nothing more than the image of a crucified man, not necessarily Jesus Christ. But the indications of a gash to the side of the body, and of blood stains near the forehead (suggesting the crown of thorns) are consistent with the Gospel accounts of the Passion, and it would be highly unusual find these marks on any other victims of crucifixion.
Although my personal belief is that it is in fact the burial (and more correctly, the resurrection) shroud of Christ, even if it is the work of human hands, the inspiration, devotion and skill to create such a remarkable and technically perfect objet d'art is to me, further evidence of presence of the Divine.