This is certainly a circular argument on the part of the speaker...as the image on the shroud was well known enought that painters have certainly long used the image to derive their view of Christ from it.
However, the iconography of Jesus that resembles the man on the shroud, predates the earliest possible date for a forgery as established by the C-14 tests by almost a thousand years. Therefor, if the image of Christ we all accept is based on the shroud... and the paintings and icons of Christ are basically the same since the 5th Century, then the shroud must have existed at least that far back.