AppleScript gives no permission error trying to open file, but the file can be opened manually
This problem is caused by Apple's sandboxing of applications (in this case, OmniGraffle). Preview does not receive an entitlement to access the PDF if you just pass it a string to open. From Apple's release notes:


  Compatibility Notes
  
  When sending commands to a sandboxed application, such as TextEdit in OS X Mountain Lion, parameters that refer to files must be of an explicit file-like type and not a bare string, or the target application will not be able to access the file. For example, file "Macintosh HD:Users:me:sample.txt", POSIX file "/Users/me/sample.txt", or the result of choose file would all be acceptable, but the string "/Users/me/sample.txt" would not.


Why does this sometimes work? When you open a file manually, the application retains the entitlement to open it (in Recents, for instance). Therefore, if you try any file you've opened already, odds are it will work, but it won't work on new files.

To fix, change your code to read:

...
    set srcFileRef to (open POSIX file srcFileString)
...