In the big scheme of things, 1.7A difference is not a whole lot when you are looking at a 6.3A reference point. And it really varies depending on manufacturer.The reference point , imo, should be the power consumption of the piece of equipment. I doubt the 6.3A is the FLA of the OP’s piece equipment. The 6.3A is more than likely a built in fudge factor the designer/manufacturer decided on to eliminate any chance of nuisance fuse blowing.
The fudge factor might be tight, maybe 110% of the FLA of a piece of equipment. It could be 125%, 150%, 175% or 200%. Maybe even 250%... It depends on the type/design of the equipment and the quality of the parts used.
Just one example. I have an ARC VT50 tube power amp. On the rear panel of the amp it is listed 330 watts power consumption. The rear mounted AC Line fuse is a dual element SLO-BLO 4 amp 250V fuse.
330 watts / 120Vac = 2.75A. The 4 amp fuse is just slightly less 150% of 2.75A.
(2.75 X 150% = 4.125)
Jim