I dunno.
I owned two of them in the late 1970s and on into the early 1980s. One was a 22-250 and the other was a 6MM Remington. I don't have any pictures of ether. I don't remember if they were stamped "Varmint Special" anywhere , but that is what they were called in Remington literature and in common discussions in gun wrags at the time, and they were housed in a BDL stock with a black fore end tip like you see still on all standard BDL rifles.
There was a definite taper on the barrel in the chamber area with pretty much a straight taper from there on to the muzzle. Maybe they did measure .820" at the muzzle, but the Varmint Special was not a straight tube rifle from breech to muzzle by any means. One unique feature on the Varmint Special rifles was a scope block that was screwed on the barrel that most users removed for a conventional length varmint scope and plugged the screw holes. Other than that the barrel was clean.
This first picture is on an early Varmint Special rifle with the pressed fleur delis checkering. Remington history shows that the Varmint Special was introduced in 1967; fleur di lis pattern 67-68, ribbon pattern 69-73, solid cut checkering 74-77, and skip line pattern 78-97. If you look closely at this rifle, you can see the short bolt shroud over the end of the firing pin that was a feature of early Model 700 riles. Later 700 rifles have a longer bolt shroud that prety well covers the bolt striker like you see today that was first required to allow standard weight 17 Remington BDL rifles to be exported to Australia.
The next two pictures are of an older generation (74-77) rile with solid cut checkering. This is the era that my two Varmint special rifles came from. Rifles built late in their production cycle had skip line checkering but I didn't see a picture of one of them.
If you look closely at the last picture you can see where the scope block was installed on the barrel. You can just see the plug screws along the barrel profile. Obviously by nature of the beast, no open sights were offered on these rifles.
And lastly a 700 Varmint Special with ribbon checkering.
The scope block plug screws from where the scope block was removed are more evident on this rifle.
Remington did at one time make a Model 700 heavy varmint model but I don't recall what they specifically called it or when it was made, but they are not the Varmint Special rifle. They were also housed in a BDL style stock.