Because the job/agent has to be given credentials to access the files. The AS Manager is usually running on an administrator PC with administrator rights, and to add a server to AS manager you have to give it authentication info. So the AS manager has rights to set up the job.
The AS Manager doesn't do the backup, the job does. So, you have to tell the job the appropriate authentication info as well.
So, to sum up, you need to authenticate as the AS Manager to see the stuff you want to back up, the JOB needs to authenticate to the sever to do the backup, and the AGENT has to be given authentication credentials by the job if there is an agent being used.