Without the original article, I can't speak for the author. However, depending on how you've implemented instantiating and opening the connection in relation to your try/catch/finally block, you might need to do some additional checking before just calling close. Ex, ensure the connection is not null and not already closed.
EDIT: The article says not to dispose of a connection object in your Finalize method, not to not close it in the finally block. In fact, in the paragraph above it says you should always be closing your connection after you use it, so it is returned to the connection pool.
"CAUTION It is recommended that you always close the Connection when you are finished using it in order for the connection to be returned to the pool. This can be done using either the Close or Dispose methods of the Connection object. Connections that are not explicitly closed might not be added or returned to the pool. For example, a connection that has gone out of scope but that has not been explicitly closed will only be returned to the connection pool if the maximum pool size has been reached and the connection is still valid.
Note Do not call Close or Dispose on a Connection, a DataReader, or any other managed object in the Finalize method of your class. In a finalizer, only release unmanaged resources that your class owns directly. If your class does not own any unmanaged resources, do not include a Finalize method in your class definition. For more information, "
http://msdn.microsoft.com/en-us/library/8xx3tyca(VS.71).aspx?ppud=4