SQL Agent Service does not have permissions to resolve UNC path

What are the proper security settings such that sqlbiagent account can access my UNC path descibed in my file connections?

When I change SQL Agent service owner; sqlbiagent, to myself the job runs fine.  When I set the SQL Agent to be owned by sqlbiagent account all UNC's fail.  Permissions to the folders have been confirmed.  The database connections do resolve and only the file connections fail.  This is a job that runs SSIS steps.  I don't want to use a proxy account as this will require a password reset over time.  

My SSIS package encyption is DontSaveSensitive and all connections are set to delay validation = True.  I'm using XML config file to get the initial connection to my database and storing connection information in my SQL table: SSIS_Configurations.

The error message is below and screen shot of permissions is attached:

Error: 2010-01-20 15:12:59.62     Code: 0xC001401E     Source: ReforecastLoad Connection manager "ReforecastLog.txt"     Description: The file name "\\hgn02\public\_Finance\FinPlan\DW\Logging\PRD\ReforecastLog.txt" specified in the connection was not valid.  End Error  Error: 2010-01-20 15:12:59.64     Code: 0xC0202070     Source: ReforecastLoad Connection manager "ReforecastLog.txt"     Description: The file name property is not valid. The file name is a device or contains invalid characters.  End Error  Error: 2010-01-20 15:12:59.64     Code: 0xC0208024     Source: ReforecastLoad Log provider "SSIS log provider for Text files"     Description: The connection manager "ReforecastLog.txt" returned an object of an  incorrect type from the AcquireConnection method.  End Error  Error: 2010-01-20 15:12:59.65     Code: 0xC001401E     Source: ReforecastLoad Connection manager "ReforecastLog.txt"     Description: The file name "\\hgn02\public\_Finance\FinPlan\DW\Logging\PRD\ReforecastLog.txt" specified in the connection was not valid.
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