That theory depends on some unknown 14th century genius (at least 100 years before Leonardo) who invented a completely new technique with the sole purpose of duping a credulous medieval population. And then completely abandoning photography after taking one photo. It also ignores the huge number of details within the shroud that no forger could have known about, or would have needed to include, to fool the public - things like pollen from thorn bushes.
It did not need to be invented. The principle of camera obscura was known and written about nearly 1000 years before DaVinci who also know about it.
In addition to resolving the issues of image size diffences between the front and back and the head/body it resolves the negative image issue.
I also explains why the physical anomaly of the hands being crossed over the groin appears on the shroud, which the human body can't do lying on it's back with it's shoulder blades touching the ground.