I puzzled on this for a bit and got sidetracked by the strange way SSMS displays statistics columns on the Property page. Then it got to be the end of the day and I went home. The next day, I had a comment on my previous post from Aaron Bertrand who mentioned there is a related bug with the stats_column_id column of the sys.stats_columns view. It does not contain what the MSDN documentation says it contains. The Connect item for this, along with a workaround, can be found here.
The script I was using did not reference that column, but it did get me thinking that perhaps the script was not correctly identifying the first column in an index.
Shaun has an updated version of a duplicate statistics checker script that you may want to check out.