Especially during Passover, when Jerusalem was filled to the rafters with pilgrims. Some nut flipping tables at the Temple and screaming about the coming kingdom of god would be dealt with quickly and harshly, lest he incite a riot. I doubt any kind of written record ever made it to Rome.
An Italian scientist has duplicated the Shroud using techniques available in the 1200s.
http://articles.cnn.com/2009-10-07/world/italy.turin.shroud_1_shroud-turin-linen-sheet?_s=PM:WORLD
The bas relief makes more sense than an actual person, just based upon the characterisitics of the image.