Kreuz uses a slightly different formula when calculating weight on the rider than on the bike. "Mass of the rider (influences rolling friction, pull-down force, and the rider's frontal area via body volume)" [emphasis added]

If you bump up the "bike weight," you'll see a much less pronounced effect of adding weight. In addition, if you have a component that is more aerodynamic but slightly heavier, the aero advantages will likely outweigh any weight penalties.

I.e. the Kreuz calculations are models that use the same assumption you're holding. This is not to say that these assumptions are incorrect, only that the calculator does not qualify as proof that they are correct.

For example: In some cases you could drop 10 pounds and, as Kreuz posits, get more aero and improve on the flats. In other cases the loss of weight may well be accompanied by and/or a causal factor in a loss in power (e.g. 2 weeks into a grand tour, crash diet).

And for my part, when I say "weight doesn't matter on the flats," I'm referring to relatively small changes in bike weight (2-5 lbs). I'm not talking about a rider healthily shedding 30 lbs over the course of a season.