This is (mostly) due to the way that inkcov works.
Your PDF file contains a transparency group with a DeviceRGB blending space. Note that this does not actually create any RGB output, it merely means that any objects which are blended must be done in RGB space. So anything not in DeviceRGB (eg all the objects in Gray) must first be converted to RGB, then blended, then converted to device space for rendering.
Because inkcov is a CMYK device, this means that the blended RGB objects must then be converted to CMYK. This results in less than perfect black. The PDF file does not in fact contain anything except gray colour specifications except for specifying the blending space of the transparency as RGB.
Looking at what Acrobat appears to do, it seems the simple solution is the one to go for, change the transparency blending space into DeviceGray as well. We know from previous experience that blending in different spaces does result in differences in rendering. On the other hand, so does changing the colour space of all the colour specifications......
Given time to do some more investigation I'll probably go down ths road in the next release.