It doesn't matter if that login doesn't have permission to show execution plans. You can query the dynamic management objects (DMO) to get the plans from cache.
But, I'll bet it has something to do with one of the table valued functions. Those things are notorious for destroying performance.
"The credit belongs to the man who is actually in the arena, whose face is marred by dust and sweat and blood"
- Theodore Roosevelt
Author of:
SQL Server Execution Plans
SQL Server Query Performance Tuning