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As root:
$ sudo python3
[sudo] password for ethan: 
Python 3.2.3 (default, Apr 10 2013, 05:07:54) 
[GCC 4.7.2] on linux2
Type "help", "copyright", "credits" or "license" for more information.
>>> import spwd
>>> spwd.getspnam("I_don't_exist")
Traceback (most recent call last):
 File "<stdin>", line 1, in <module>
KeyError: 'getspnam(): name not found'
>>> spwd.getspnam("bin")
spwd.struct_spwd(sp_nam='bin', sp_pwd='*', sp_lstchg=15259, sp_min=0, sp_max=99999, sp_warn=7, sp_inact=-1, sp_expire=-1, sp_flag=-1)
As normal user:
$ python3
Python 3.2.3 (default, Apr 10 2013, 05:07:54) 
[GCC 4.7.2] on linux2
Type "help", "copyright", "credits" or "license" for more information.
>>> import spwd
>>> spwd.getspnam("I_don't_exist")
Traceback (most recent call last):
 File "<stdin>", line 1, in <module>
KeyError: 'getspnam(): name not found'
>>> spwd.getspnam("bin")
Traceback (most recent call last):
 File "<stdin>", line 1, in <module>
KeyError: 'getspnam(): name not found'
People can be confused. How could the name not found if the name actually exists?
Attached the patch to differentiate the error whether the error is really 'name not found' or 'permission denied'.
I use the error message from the getspnam manual:
http://man7.org/linux/man-pages/man3/getspnam.3.html
There is another error message from getspnam beside EACCES (permission denied), which is ERANGE, but I don't think we need to handle this.

PyErr_SetFromErrno(PyExc_OSError) looks more appropriate for permission denied error. However this change is backward incompatible so perhaps we have to left a KeyError.

Attached the patch to accomodate Serhiy Storchaka's suggestion by using KeyError exception for backward compatibility.

It was not a suggestion, it was a doubt.
See also issue10388.

Sorry about that.
Okay, so for now, we wait for other people's suggestion, which way we should use to handle this situation?

I think we should always raise OSError if errno is non-zero (and not KeyError).

Sounds like we want something analogous to http://bugs.python.org/file33404/fix_error_message_getspall_v2.patch for this bug. Moving to patch needed.
It looks like it would be easily tested too, so I'd like to see a test too please.

Here is a patch with a test.

As far as this change breaks compatibility. please add a note in the "Porting to Python 3.6" section in What's New.

New changeset a1d738158390 by Berker Peksag in branch 'default':
Issue #18787: spwd.getspnam() now raises a PermissionError if the user
https://hg.python.org/cpython/rev/a1d738158390 

New changeset 430af393d8f1 by Victor Stinner in branch 'default':
Try to fix test_spwd on OpenIndiana
https://hg.python.org/cpython/rev/430af393d8f1 

New changeset c1677c8f92e1 by Victor Stinner in branch 'default':
Fix test_spwd on OpenIndiana
https://hg.python.org/cpython/rev/c1677c8f92e1