The REMINGTON stamp simply indicates that the barrel blank was supplied by Remington. Remington supplied barrel blanks, locks, and other parts to the gunsmith's trade for many years, prior to manufacturing guns of their own on a large scale.
C BROCKWAY might be the maker, but I think LEFEVER & ELLIS are just as likely, especially since this rifle has a lot of New York state features, such as the single (brass?) trigger and lack of an underrib for the ramrod ferrules. Daniel M. Lefever and James H. Ellis were partners in Canandaigua, New York, from 1862 - 1867. They produced some fine heavy target rifles.
So.....if Brockway made the rifle, Lefever & Ellis did something to it later on, such as re-cutting the rifling, OR...if Lefever & Ellis made the rifle, Brockway did something to it later on. It could go either way.