Kris and Amber,
I had the same problem, and I found a solution that I'm guessing both of you figured out eventually.
The main issue is that the error message about admin permissions is misleading. It's not referring to the permissions you have to write to a local directory, it refers to permissions of changing the name of the SWAT Parameter Geodatabase.
For example:
SWAT2012.mdb
That is what happened to me at least. I didn't fully understand what the role of that database at first and tried to rename it "SWAT2013.mdb" or "SWAT2014.mdb" and that's when I received the permissions error. Moreover, once I received that message the original directory I was trying to set the project up in became corrupted and even changing the name back to "SWAT2012.mdb" did not alleviate the problem.
If this happens to you simply create/choose another directory to set your ArcSWAT project up in and do not change the SWAT Parameter Geodatabase in the first place.
Booya.
- Sam