I agree with that notion in general, and here's some of the reasoning:
The lower drop on the sides is effective because the front wheels are relatively close to it and extend the furthest into the airpath, whereas what undercarriage extends down is typically further back and far less of an addition to frontal area.
At some point, any protrusion into the airflow creating a vortex or turbulence has an area behind it at which the air resumes less turbulent flow. For lack of formal education on the matter, I'll call it a turbulence envelope. Anything inside this turbulence envelope is unlikely to cause additional disruption or significant drag, and might even reduce it. Anything outside or beyond the tail of the turbulence envelope is effectively an additional surface to create turbulence and drag of it's own.
In a nutshell, the lower side dam is probably effective because the nearby tires are partially within the turbulence envelope, whereas things like suspension parts, oil pans, exhaust, etc. are too far back to remain within it.
I think that the flow pattern of the air with a lower dam on the sides is another issue to consider as well, as with a raised center and open area to the outside of the car, it creates an even larger area for the envelope to exist around the wheels. A flat across air dam by contrast likely propagates a rolling vortex underneath the undercarriage that does not provide the same drag reduction around the wheels.
This difference in behaviors would explain why fuel economy might improve with lower sides, and down force might improve with a lower center, as the lower sides do nothing to slow the airflow under the car, but the lower center does so by
creating turbulence. In other words, it would seem that the two goals would be difficult to achieve together with an airdam alone. But that's where belly pans come in.
Obviously this is just my 'feeling' for the dynamics of it, but I think it's pretty close to the reality of what is going on.