Well, first, what I mean by "altogether" is that just the portion of a fiducial that lies over a very bright background is no longer visible against the background. That doesn't mean you still can't see other parts of the same fiducial that happen to lie over a darker background. The goal is to understand the mechanism by which that might occur in a typical workflow for the digital images released a while ago, that some hoax claimants have used to say the images were composed.
In my experiments, overexposure on the film wasn't enough to cause the effect, although the fiducial was dimmer. Scanning didn't contribute to it. Even reductions in resolution using common algorithms and error diffusion didn't make fiducials over bright spots disappear. Finally it was JPEG-style image compression using something like a 75% quality setting that caused the faint fiducial segments to become completely invisible on a white background. As this would not be an atypical workflow for processing images to release as a convenience on the web in the 1990s, I consider the hypothesis suitably supported by evidence.
As for reasons in general why someone would not want fiducials in the picture, there are various artistic and editorial arguments. But in those cases, the fiducials are removed entirely, probably by digital editing.