That is as intended, the bayonet should be to the right side when fixed to the muzzle, not underneath where it would interfere with the removal of the ramrod during loading. In addition, the bayonet needs to be off to the side so the soldiers could stack arms. A snug fit is probably intentional as you will note there is no locking ring to hold the bayonet in place once it is fixed to the muzzle. These were not machine made parts interchangeable arms so a bit of fitting to the barrel is also not uncommon or unexpected.
The .69 caliber bayonet was the same for the entire run of US 1816/22s. The bayonet lug was later moved underneath the barrel for the redesigned US 1835/40 muskets. This required a different bayonet configuration for the later models because the lug underneath the barrel would have the bayonet on the opposite side when fixed to the muzzle.