What a gorgeous rig. The story is bunk IMO, and I've seen the same story on eBay many times. Agree with Brett, bowtie on grill is aftermarket too. the 350 on the grill is way too bright also. mis-matched screw on the steel panel under the steering column. Check the oxidization on the edges of the emblems, 40 years in a garage and they should be unmarked and un-pitted.
Nobody buys a K5, then brings it home and mothballs it. Ever.
I recently bought a car that had been in a garage for 47 years. It was driven for 9 years first though, and the reason it ended up in a garage was due to a wreck. Solid yes, and perfect for my wants...and the story makes sense. This K5's story makes no sense.