Scope of functions for invocation by module_invoke_all seems to not include .inc files

A contributed module that I am using [popup_forms] uses module_invoke_all to check whether any modules have defined a form for it to use.

I have defined the necessary function called mymodule_popup_forms_data() that provides the information that popup_forms needs.

If I locate that function within mymodule.module, all works well.

If, however, I move that function to a mymodule.inc file, then the module_invoke_all in popup_forms does not find my function.

This despite trying a very large number of variations of module_load_include, include_once etc. etc. etc. I think that there might be a hint to what is going on in a greg.harvey comment five years ago:

"Worth noting, if you want to include data (e.g. a views object) in an include file, you cannot use this function - because the data will only be available within the scope of module_load_include() function, not within your own function that invoked it."

Hence the question: Is it true that a function defined in a .inc file that is included via a module_load_include call will not be "in scope" for module_invoke_all?