SQL Server: How can I read server-side traces with limited permission?
To view the trace file contents in SMSS, I am using the following function: FN_TRACE_GETTABLE. To run FN_TRACE_GETTABLE, the users don't need any permissions on the server's file system. Only the account that is running the service must have the permissions to access the trace file, but it already has them, because it has created the trace file in the first place.

I have an automated job that uploads a trace file into a table every weekend, and neither me nor the account running the job have any permissions on the server's file system. This is running 2008 R2.

When I was developing that job, I had run FN_TRACE_GETTABLE from SSMS quite a few times.