You definition is correct... however...
Don't be so 'exact' when dealing with others....
If you are not referring to the same thing then communication breaks down because you are talking past each other. Therefore, a similar understanding is necessary for any productive conversation. If that similar understanding is inaccurate, then you are engaging in and furthering disinformation.
It is exceedingly easy to use language to mislead. Therefore, if one is truly interested in the truth, accuracy of language and understanding of ideas is very important.
As you have said before, you need the gray areas. When accuracy is expected, your arguments break down.