Documentation says filtered indexes automatically include primary key, that is incorrect by Tom Cooper

The documentation (http://technet.microsoft.com/en-us/library/cc280372.aspx) states in the Limitations and Restrictions section: "The primary key of the table does not need to be a key or included column in the filtered index definition. The primary key is automatically included in all nonclustered indexes, including filtered indexes."

That statement is not correct.

As with all nonclustered indexes, the keys of the clustered index (if any) are included in each nonclustered index (whether filtered or not), but the primary key column(s) are not included unless they are in the clustered index.