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 might try, on hardware or emulation: Poco (modern macOS), Blue Paint (classic Macintosh), NewtPaint (Newton), MoePaint (Palm), CHEESE 2 (MSX), Airbrush (PC-100), Ink Pot (PC-88), ESQUISSE, Multi Paint System, Z's STAFF (PC-98), GraphicsGale, Easy Paint Tool SAI (Windows 9x to current), JINZO Paint (Windows CE, I picked this up recently to added fixes and new features), Matier, Full Color Paint Tool SAI, G-TOOL (X68000)
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.