So for someone who is writing office document, Microsoft Word is the OS?

I think your definition attempt renders the term Operating System useless.

We have pretty good definitions of 'operating system' already, no need to invent new useless ones.

The popular packages are properly described as "GNU/Linux." That we deem their combination to be an operating system is a matter of convention.

When an Emacs user greps from Emacs why is this less blessed than my grepping from Bash? Is it considered blasphemy against vi?

Yes, I see that Bash is not the OS and vi is not the OS and neither of course is grep, for the OS is the turtle upon which these things rest and it is turtles all the way down until you get to microcode. Just because someone calls themselves "a computer scientist" it does not make their abstractions are any less metaphysical.

It is when we use an human centered definition of "operating system" rather than a machine centered one that Emacs can be seen in a different light. It is not that either group is failing to develop a scientific model. It is that each model has orthogonal metrics.

"So for someone who is writing office document, Microsoft Word is the OS?"

If the computer is never used for any other application, then that's an arguable position.