I think that's right. Paint programs might give you the "broad strokes" (so to speak), fill areas — it's clear the dithering on an arm, for example, was done a pixel at a time.

I spent many hours in "fat bits" mode in MacPaint creating B&W game artwork for early shareware games I wrote. Click a pixel to invert it.

Not in Japan, you can see how the dithering was done in the video I link below, which was taken from promo footage of one of the most famous period Japanese paint apps for PC-98: Multi Paint System (1992, by Woody_RINN). The artist would paint two colours and then use a dither blend tool along the contrasting edge. https://youtu.be/nIdFor2WOnw?t=430

I'm sure some people did it pixel-by-pixel, but not so much in Japan where the software was designed to make dithering like this very easy.

You can find my big list of Japanese pixel art apps at: https://news.ycombinator.com/item?id=41136905