Your "wrong index" is the clustered index. Since SQL Server needed to go to the table for the additional information not included in the nonclustered index (the "correct index"), SQL Server decided it was cheaper to do an INDEX SEEK on the clustered index rather than an INDEX SEEK on the nonclustered index with a bookmark lookup to the data for the additional information.

Looks to me as if SQL Server used the "correct index" where you believe it used the "wrong index" for the second query.