Typically when you buy a fixed reamer you can ultimately specify/order any final hole size that you require, if you want. However a standard 'off the shelf' reamer that you may (probably?) have might typically produce say an ISO H7 class of hole fit which is a close clearance on the nominal, around a thou up on an inch hole. I question if your pins are "exactly 1 inch". If they were manufactured from standard ground shafting they will most likely have a very small minus tolerance. A good micrometer will confirm all of this.
Just my opinion but the actual clearance you end up with is subjective and often described (as you did) rather than quantified. The clearance needed to get that 'described' fit with an adjustable reamer may be different dependent on the final axial alignment of the bushes, should there be any distortion of the tubes. So who really knows what the resultant radial clearance will be after reaming without some very precise post reaming measurements or a session on a coordinate measuring machine. Rightly or wrongly I've made my bushes 2 to 3 thou over size but hopefully they will be reasonably axially aligned to each other after bonding.
Again just my opinion but... You might struggle to get the fit you require with a fixed reamer and particularly if there is any weld distortion in the tubes.
The man that really knows all of this of course will be Arwyn
Good luck!