Not really. The embossed certificate artifact from HI showed his birthplace in HI in the reporters digital photos of that artifact.
The layering could be the result of the WH manipulating the image to show what they wanted it to show.
There are digital photos of the actual artifact from HI. They weren't the greatest shots, not forensic quality, but they show the data in the digital scan on the website (with the layers) and the embossing. To get those photos the WH would have scan the artifact from HI, alter, print, emboss, etc. That would require time and prep, so in fact the only feasible story is they threw the paper that was sent from HI in the trash and brought out their own forgery on official paper, forged signature, embossing, etc. that they created well in advance.
Much more likely possibility: the paper from HI was displayed. It was scanned and layered but not altered since the contents match the digital photos of the (alleged) paper from HI.
“To get those photos the WH would have scan the artifact from HI, alter, print, emboss, etc. That would require time and prep”
If anyone could do that, surely it would be the holder of the Oval Office.