Although it's true that a standard FL sizer may reduce body diameter when backed off a bit (less so with a strongly-tapered case like the .303 than less-tapered designs), a proper neck-size-only die is made with enough clearance to avoid the body entirely
I see - that'is what causes the neck not to be concentric to the body. Never used one - always just backed off a FL die. If this rifle is chambered for .303 Epps Improved, a custom FL die will be need.
Some do, some don't; some will, some won't; I might ...