Yes, it is the same rifle. I bought it from the owner listed in the book

... Joe

Bringing this old topic back up, mainly because I have some evidence that answers some questions listed above, and some answers to incorrect assumptions or statements made above.

The first Creedmoor match was held in late Nov. 1874, and Remington did not catalogue their Long-Range rifles until 1874. But the challenge by the Irish was made almost a year earlier, and even before the 1874 Match Remington and Sharps began work on producing these rifles. Prototypes of the rifles to be used at the match were made  and sold in 1873, even though they were not a catalog item in 1873.
The Remingtons used in the Creedmoor matches were in the low 3000 serial number range. But there is at least one Creedmoor rifle with a serial number in the low 1500 range! George Armstrong Custer was also given a Creedmoor in this same range. His was #3333, and Fulton's was #3310. 
The .44-77 Remington-Sharps Bottleneck was deemed too weak for 1000 yd. duty. So the 400 gr. bullet was replaced by a 535 gr. paper patched bullet, and the throats were opened up so the 535 gr. bullet was barely seated into the case neck, and 90 grs. of powder was the charge in the case. This was done before the Creedmoor ever saw use in the 1874 match as the guns built as prototypes in 1873 will also accept the 535 gr. bullet barely seated into the case neck.
Almost all the Creedmoor Rolling Blocks were half octagon. But Fulton's was a full octagon, and still fit into the 10 lb. weight limit of the rules. Two others are known of in full octagon, and not sure of others?
There are at least three in full round, which Joe's is one. I own one of the others, and mine is one made in 1873 with a serial number in the low 1500 range, well below the ones used in the Creedmoor Match.
The heel sights were offered right from the very beginning, before the Creedmoor match took place in Nov. 1874. The way the sights were attached changed numerous times, but some rifles got no heel sight accommodation at all. It depended on the customer's request for one or not. I've seen heel bases simply wood screwed into the stock. Other's done like Joe's where an ebony insert was first inlaid, and then recessed for the base. And some that had a steel insert inlaid into the heel position, and the sight mounted with machine screws exactly like the tangs used.
Wish I knew of any records of serial numbers for the other rifles used in the 1874 match? That's probably the only way we could ever confirm provenance of who owned what.