Hm, just trying this and maybe I am missing something here. I thought the remote raster image "vader1.png" is such a 1-bit image (see the last example at https://docs.generic-mapping-tools.org/dev/image.html#examples), but using I=True does not flip the black and white pixels as expected:

import pygmt

fig = pygmt.Figure()
fig.basemap(region=[-5, 5] * 2, projection="X3c/1c", frame=0)

fig.image(imagefile="@vader1.png", position="jLM")
fig.image(imagefile="@vader1.png", position="jMC", bitcolor=["gray+f", "blue+b"])
fig.image(imagefile="@vader1.png", position="jRM", I=True)  # Does not do something
# fig.image(imagefile="@vader1.png", position="jRM", bitcolor=["black+f", "white+b"])

fig.show()

Same for

gmt image @vader1.png -I -png image_I_gmt

Hmm, it looks like an upstream bug.

I tested it with the gmt dev version, and still no inverted colors. Thus, I wrote an issue report at GenericMappingTools/gmt#8795.

The upstream bug has been fixed.

I've added a note in the docstrings.