New answers tagged check-in
As commented by Robert... first check if there is any workflow or feature attached with the document library that might be altering the user permissions. The user must have at least read permission to the document library in order to access it. The item level permission may differ. Example... the user can have contribute permission only on 50% of the ...
You don't need to give read permissions to the entire library, just to this item. IMHO is to verify the permissions one more time. You can find the permissions levels at http://technet.microsoft.com/en-us/library/cc721640(v=office.15).aspx Also check, in list settings/versioning settings/ who can see an item.
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