"That's not completely true" comports with "There's a theoretical truth and a practical reality". Since we're talking about practical matters, a theoretical truth isn't completely true if it's not also practically true.
Maybe to you, but not to me. "That's not completely true" also comports to mean that something that some one calls true, as being mostly true, but not entirely. So be clear, so I don't have to try and assume what you mean. If you can't do that, don't expect me to do it.