Tom, I can see how all this conflicting information can be confusing.
On the first link you posted, they said:
With planted tanks, and there is a small fish population, even agitation is kept to the minimum, to actually keep CO2 in.
What they are saying is that if you don't have a large fish population to supply CO2 to plants, then you want to eliminate surface agitation to prevent CO2 loss. A planted tank with a heavy bioload of fish can supply a pretty good amount of CO2 to a moderately lit tank.
The second link you posted mentions this:
There is a gas exchange which takes place at the surface of the water between carbon dioxide (CO2) and oxygen. The exchange results in carbon dioxide (CO2) leaving the water and oxygen entering due to the fact that there is more oxygen in air than water and vice versa for carbon dioxide.
They are saying that CO2 levels are higher in the water than in the air. This is not always true. It certainly isn't true for a CO2-injected system, and it isn't generally true for a cup of standing water (unless it is carbonated, hehe). But it is true for that planted tank we were talking about that has a heavy fish load. All those fish are releasing CO2 into the water and you could see higher CO2 levels in the water than in the air. In this case, aeration would cause you to lose that CO2 more rapidly.
In a low-light tank with low-light plant such as some crypts, anubias, java fern, etc. I generally will use surface agitation. It keeps things consistent. You'll usually see CO2 levels around 3-4ppm. You won't see fantastically rapid plant growth, but under the right conditions, plants can grow healthy and lush nontheless. Without the surface agitation, and with a high fish load, you might see CO2 levels around 4-6ppm, but then you have to worry about the consequential nutrient output of the fish, and the plants inability to consume those nutrients, given the CO2 and lighting conditions. Your best friend in that case is water changes to keep nutrients in check.
It's confusing at first, but once you understand, you'll be more well equipped to care for your plants. Never hesitate to ask questions!