Howdy!
Will, what FCK is referring to has to do with the Henry's unique mag tube that is machined from the barrel blank. I said "unique" and there MAY be another gun or 2 made that way ... but I don't know of any.
Any-hoo, your hand will allow the barrel harmonics to do their thing with minimal effect on the harmonics. Put it on a solid rest and the game changes - apparently for the worse! Those Italian Henrys have a great reputation for accuracy, and it's all because of the stiffness of the barrel/mag-tube assembly.
Under these situations, I'd consider perhaps a rest, but with your hand doing the actual resting on the support: you know, rest on the bench then hand placed on rest, then rifle placed over the hand so that our hand is between the mag-tube and the solid (to the bench) rest.
Perhaps a better idea is the way Driftwood and others have suggested already!