Dmin is base + fog. Dmin is the term used for that by photo engineers just as they use Dmax for the maximum density in a curve.
Lets assume that we have 2 curves which are identical with base + fog removed. Imagine it. Now, add fog and the one with higher fog has higher Dmax as well. This is a 2 way street of deception. It can work the other way too.
The correct way to present a sensitometric curve is with base + fog or with Dmin shown. Sorry, but that is the fact here and the fact that removes any possible error in interpretation.