Good conversation guys. 
You are all correct, but you are talking about different things.
Fluids are in the liquid state or vapor state.
In the liquid state capillary action occurs. As Bob posted from USGS, it is about the movement of water (liquids) due to the forces of adhesion, cohesion, and surface tension.
In the vapor state, moisture moves due to pressure differentials (Delta P).
This differential is addressed by Psycrometrics (HVAC Stuff etc). Just as higher temperature always moves towards to lower temperatures, higher pressure moves to lower pressure. Also keep in mind that very moist humid air is lighter than air without as much moisture.
Be aware that what was posted here from the web about the state of moisture/vapor pressure is about that happens in a closed container (like HVAC systems). In an open container the molecules in the gaseous phase will just fly off and the equilibrium talked about here would never be reached.
Yes, that is exactly what is happening. Someone mentioned “pushing” water. It’s more like sucking.
So, lets forget about everything discussed so far, and focus on an “Open Container” situation. When liquid and vapor are in a closed container, with a stable temperature/pressure, molecules are changing state from liquid to vapor and back continuously, and at the same rate. When liquid evaporates it gets colder. Being colder it simultaneously condenses. This is not the case in this thread.
“It sucks” 
We said high temp always moves to cooler temp. Well, the dehumidifier makes it hotter in the crawlspace.
This heat allows liquid to evaporate faster than condense, breaking the equilibrium. The dehumidifier makes a cold coil through refrigeration and condenses the vapor and moves it out of the CS. What is removed, must be replaced. This basically creates a vapor vacuum in the CS (to make it simple) which changes the surface tension allowing more liquid to change state to a vapor. What does this do? It causes the CS side of the foundation to give up heat and become colder. As we said, heat moves to cold. When the inside surface is colder than the outside, movement will be inwards. Again a Delta P is created, liquid turns vapor, and liquid will replace itself. Keep in mind moisture is heat (970 Btu/Lb).
So looking at this chain reaction, moisture is actually being pulled into the CS by the psycrometric changes the dehumidifier created.
For you guys who deal with Mold, if you have mold in a CS where there is a dehumidifier present, you may notice that there is a pattern to the mold throughout the CS. Mold will grow and create a pattern away from the dehumidifier location. This is from moisture entering the CS where it is cool enough to condense moisture from the outdoor Air entering the space. Mold may be on just one side of a joist, or there may be more growth in one area over another etc. If you are in the mid-south, this is very evident.
[quote=“Christopher Currins, CMI, post:8, topic:221269, username:ccurrins”]
So actually having a dehumidifier in a basement may not always be such a good idea.
[/quote] 
This can be a case of “A little can be good, but more is not better.”
We want to control moisture in the space at acceptable levels without pulling all kinds of moisture through the building envelope where moisture will really cause the water damage. If the CS becomes dryer than the interior of the house, where do you suspect moisture will be pulled from? There is an Air Conditioner up there operating below the dew point temp of the outdoor air. Supply ducts are located around windows that are primary leakage points. What happens on the inside of the wall there?
We have a problem in the Nashville area where building codes are requiring improper sealed crawlspace and dehumidifiers are installed. Mold in new construction…
As for mediation; psycrometric testing can identify this condition.
Hope this helps.