These statements are all incorrect.
There is no such thing as "CN3"; this is likely a poorly-remembered confusion of "C3" and "CN", which are two different bearing "pre-fit" clearances, in addition to C1 and C2.
CN, C1, C2 and C3 are different (but overlapping) internal clearance ranges before the bearing is mounted, one is selected not for either "pre-fit" or "mounted" clearance (the latter fitted but before operation) but to achieve the correct clearance in operation at a stable temperature. Operating clearance is different for different bearing types.
Mounting affects the internal clearance of any bearing - interference-fit in a crankcase compresses the outer race, reducing the bearing's internal clearance; interference-fit on any shaft enlarges the inner race, also reducing the bearing's internal clearance; otoh, slip-fit on any shaft doesn't enlarge only the inner race, so the bearing's internal clearance won't be reduced by that. So the fit of a ball- or roller-bearing on any shaft - crank, axle, etc. - absolutely does affect the bearing's mounted and operating clearances.
To my certain knowledge, Triumph used CN, C2 and C3 at different times on the same/similar engines and at the same time on different engines. Nevertheless, what Triumph did or didn't do half-a-century ago is irrelevant to a rebuild now, particularly when the history of the component isn't known. Longevity is likely most desirable in a rebuild now, so selecting the correct pre-fit clearance to achieve correct operating clearance in the new bearings after the rebuild is the essential.
A new bearing's pre-fit clearances might be the same as the replaced bearing's, if the component is low-mileage and previously-unrebuilt; but something as simple as stretching of the ally around a crankcase bearing housing will alter how much compression it applies to an interference-fit main bearing, altering the "mounted" and "running" clearances of the bearing.
The correct method is to measure both inner (crankshaft?) and outer (crankcase?) bearing mountings, then select CN, C2 or C3 as required for the bearing type. Then, especially if a bearing is interference-fit, DO NOT drive it in/on cold, heat either the outer mounting (crankcase?) or the bearing itself 'til it slips into/ on to the mounting.
Operating clearances
Certainly according to SKF, a ball-bearing should operate virtually without clearance; roller-bearings of all types usually require a little clearance. Too little clearance in both ball- and roller-bearings causes the balls or rollers to 'skate' over race surfaces; too much clearance allows balls or rollers to 'chatter' between the races; too much clearance in a ball-bearing on a crankshaft could prevent it locating the crankshaft correctly.
... but ensure you are not reading nonsense?
So you want to buy the correct bearings first time?
