Sorry, I hadn't noticed that this was all being run locally, so no, network guy is the wrong person.

If, however, the OP can use DTExec to do it, this still likely points to Kerboros Double hop. Even if you are running locally (SSMS on the same Machine as the SQL Instance, which, in turn is the same machine the file is on) the double hop issue will still arise. The credentials are still going SSMS->SQL Server->File System, it doesn't matter if it's all the same server, at the point of SQL Server-> File System you're at the point of the "double hop". I would put money on betting that if the OP tried to execute the task via Agent it would also work.

I'm not going to lie, I have no idea on how to resolve the matter of the double hop. Sorry (I realise not being helpful there). I am, however, intrigued to hear if it does work via Agent (as I suspect).