Isn't this note outdated?
"You must close the NetworkStream when you are through sending and receiving data. Closing TcpClient does not release the NetworkStream."
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Could you clarify? What makes you think the note is outdated?
It looks like TCPClient.Close method disposes the NetworkStream :
https://referencesource.microsoft.com/#System/net/System/Net/Sockets/TCPClient.cs,e70aabe5304f5cb1
Also TcpClient.Close document states that "Calling this method will eventually result in the close of the associated Socket and will also close the associated NetworkStream that is used to send and receive data if one was created."