[oh_my_goodness]

>The trick is that all of this is true no matter how you partition phase-space. Though that does mean that what is and isn't a high entropy state depends on your perspective.

That seems to be correct.

>Yeah the author is conflating low entropy with a low number of microstates

Since entropy is found by counting micro-states (for example your third paragraph), that should be ok. What am I missing?

[contravariant]

The equivalence is an important theorem (important enough to be engraved on Boltzmann's gravestone), and if you're switching back and forth in an explanation of what entropy is then you're skipping over some important details that answer what it means for something to be a 'low entropy state'.