It probably wouldn't take much of an investigation to determine if inquiries were made regarding the actual value and authenticity of the painting, by any of the three "investors".
No it probably wouldn't much of an investigation.
But it could only be done by law enforcement.
Internet search records along with when would be key.
The 3 buyers knew that they were buying something special. More than likely they saw it at a preview, got together some money and went after it at auction. It happens all the time. We attend auctions irregularly. Many of these antique buyers go to yard sales and come up with unbelievable things. The seller has no clue that the ugly vase from a dead aunts apartment could be worth thousands when they put that $25. sticker on it. This is a lesson for anyone clearing out attics and basements of deceased grandparents and others. When in doubt have the stuff appraised. It will cost a bit but not as much as this "find" in NH.