When you call SqlConnection.Dispose(), which you do because of the using block, the connection is not closed, per-se. It is released back to the connection pool.
In order to avoid constantly building/tearing down connections, the connection pool will keep connections open for your application to use. So it makes perfect sense that the connection would still show as being open.
What's happening after that, I can't explain offhand - I know that keeping a random connection open would not cause that, though, because your application can certainly make more than a single concurrent connection.
