Shimming the input pinion coul still be needed though.
Even if you have no side to side play the teeth could be still making contact on just the tips, this will also break teeth, but you can not feel it as the lash is minimal.
I have had instances where I shimmed the input pinion inwards, and then having to shim the diff itself towards the left (so adding a shim on the RIGHT)
Always check for as much tooth on tooth contact as possible.
Thats why I usually remove the bulkhead from the chassis, that way I can look into the housing from below, and ensure the pinion and diff gear have as much contact as possible.