I was performing a Site Backup task for a customer's SCCM 2012 SP1 platform today and I came across a peculiar error.
I had shared a folder locally and given both the computer accounts of the site system server and the remote SQL server read/write share permissions and Full Control NTFS permissions to ensure it ran through successfully.
Tip - In order to start the backup manually you can start the SMS_SITE_BACKUP service, instead of waiting for the allocated time.
Even though everything was set up correctly I received this error:-
Backup folder does not exist or backup service does not have permission to access the folder.
As per this article from Microsoft (ref - http://bit.ly/1jy2wum) I created a subfolder inside the UNC path and repointed my backup task to it.
Low and behold after rerunning the backup job, it succeeded without any errors!
Looks like the note of "NOTE This issue is schedule to be addressed in Service Pack 1" on the MS article may have been slightly off the mark...
Hope this helps.