I haven't heard that theory. Three different papers, different weights and colors? Hmmm...
In order to entertain that theory, I would have to somehow rationalize the consistency between (let's make it simple) the two best photographs (in terms of resolution and focus) which show the seal from the front, namely factcheck #1 and #5. Photograph #2 is also of sufficient quality to throw into the mix. The consistencies I refer to are small-scale features such as tiny creases, relative heights of the individual line segments that make up the paper deformations of the raised seal, variation in height along any one of those line segments, and the location of the paper background pattern with respect to the raised line segments which make up the seal (as well as features to the outside of the seal, such as small bends and defects in the paper, which would also have to be "reproduced" from document to document if in fact more than one piece of paper was used). For "reproduced", we can consider both physical manipulation and image manipulation, either one of which is a modestly technical feat (challenging, but not to be ruled out. IMHO unlikely in this case).
If I were to attempt to provide a set of digital images that would exhibit a high degree of consistency in terms of such features (and for argument's sake, let us say that the supplied factcheck documents are of medium degree), I would probably have to consider mocking up a 3D seal and then use the usual graphics tricks (Pixar-esque to coin a term that will probably never be repeated) in order to provide a superimpose'ble seal that would be suitable for use at different angles. But if I were to go through all that trouble, it would be silly to try to marry such a digital construction to a physical piece of paper when it would be so much less risky to simply model (mock up) the document itself as a designed/virtual object along with the seal.
That is my intermediate working conclusion. I have a few more chores to do on this task.
I urge you to take the time to look at those images again, keeping the above in mind. Don't be distracted by differences in coloring; the key would be in the location of highlights on the individual bumps (which together with focus are probably the main cues for assessing or building up the mind's representation of a three dimensional object in the absence of a stereoscopic view).
I'm not ruling the three-paper theory out, but I think that I will await a report of your re-examination of the images before I persue it, because at this point I think that the time I took took to share my observations with you are a fair exchange. (That is not meant to be snarky). If you believe that they are of no value, then I guess we have concluded our business on this topic :)
I have been following your work on other topics, and I do value your opinion.
For those playing at home, this is a portion of #5. The #1 image is much more detailed, but too big to post. There are regions of the seal that are fairly well in focus in both images, if you want to compare features. The tiny creases along the paper fold are especially fun. Brownie points to the discoverer of paper fibers and such!
FYI . This post and the ones preceding it. 
At the very least, I think one could conclude that the position of the seal on the photographed document was a "done deal" before the scan was made and posted ... and that is probably much too conservative of a conclusion :)