Inconsistent behavior for Me keyword
That is a bug.
According to MSDN:
Me provides a way to refer to the specific instance of the class where the code is executing.
To me this means that it should always be the new document. Ensure that you aren't running the code in the template by accident.
SOURCE:https://msdn.microsoft.com/en-us/vba/language-reference-vba/articles/me-keyword