Emacs manual §31.28 says this about before-change-functions and after-change-functions:

These hook variables let you arrange to take notice of all changes in all buffers (or in a particular buffer, if you make them buffer-local).

That sounds like exactly what I need to monitor the status of the *Messages* buffer, but there is a note in the manual that says

Output of messages into the *Messages* buffer does not call these functions.

What is the significance of this message, and how can I set up functions that run every time the *Messages* buffer is modified?