He's saying that you have two air conditioners: one that vents heat inside your house and one that vents heat outside your house.
Your dehumidifier and your air conditioner are mechanically identical. The only difference between the two is where the waste heat goes. The exact same device is called a 'dehumidifier' if the waste heat is vented indoors and an 'air conditioner' if the waste heat is vented outside.
There's not really any efficiency gains from running a dehumidifier to reduce air conditioner use. They both use the same power and have the same effect on the absolute humidity, so you might as well just run the air conditioner (unless you want it to be warmer).
There's also dessicant dehumidifiers that don't use a refrigeration cycle. They do also warm the air a bit but may be more efficient per mass of water removed from the air, depending on the temperature and humidity range.
I do have an air conditioner (well, an air-source heat pump), but it doesn't adequately remove enough moisture before the indoors gets too cold. It's possible this is not properly sized, but I cannot change it because I rent.
In my case I did some tests, and the additional power usage of the dehumidifier is way more than offset by the power savings I realize by running the air conditioner less frequently. This only works because the dehumidifier enables me to be comfortable at a higher indoor temperature.
Because it's less humid, I can maintain a higher indoor temperature and still be comfortable, meaning the air conditioner needs to run less.
Do I use net less energy? In my case, yes, but your mileage may vary depending on your equipment, insulation, etc.