Yes, it is like they say in that website. For a monopole, the connection at the antenna is that the center conductor is connected to the base of the radiating element, and the outer shield of the cable is connected to the ground plane. For a dipole, the center conductor is connected to the base of one of the two radiating elements, while the outer shield of the cable is connected to the base of the other element.
It might be confusing if you think that the shield of your coaxial cable is a ground connection. Many beginners think of "ground" as a place where there is no voltage and no resistance, a place where all the current goes to disappear. At radio frequencies and especially on transmission lines like coax, there is just as much current flowing on the ground wire (the shield if we talk about coax) as there is in the center wire. The shield isn't really a "ground" at all, its just the second conductor in a two conductor cable. In the same sense, the outer shell of your radio transceiver is not an ideal ground either. It may be connected to the ground wire in the wall through its power cord, but that doesn't mean that the high frequency voltages and currents are zero at the radio chassis.
There is a kind of magic in coax cable. Its not really magic, but until you understand the physics of it all, it does seem that way. You see, the electrical energy is flowing inside the coax, but not on the outside (in the ideal case). Where the coax connects to your radio, the outside of the radio case has no high frequency voltages or currents on it at all, so you can touch it and nothing will happen. But inside the metal case the high frequency currents and voltages exist on the inner wall of the metal housing. When you connect a coax cable to this box, the energy inside the metal housing can flow to the antenna by conducting on the outside of the coax cable center conductor, and on the inside of the coax cable shield. In the ideal case, it stays inside the cable and does not leak out. This remarkable behavior is the result of the skin effect, which is something you can look up and study. The skin effect is what we call the behavior of high frequency energy to stay on the surface and not penetrate through solid metal. Anyways, the same thing happens with signals picked up on the antenna. They conduct into the inside surfaces of the coax cable and down to the radio chassis, staying always on the inside (in the ideal case).
The connection between coax cable and a monopole is almost ideal because the current flowing on the inside of the coax shield doesn't have to go through any tight spots to flow out onto the ground plane, because the shield touches the ground plane all the way around the base of the radiating element. The dipole, on the other hand is not an ideal connection to coax cable. When you strip the end of the coax to prepare for connection to the antenna, the shield must be reduced to a wire and then connected to one element. This is a compromise connection, and not ideal. We call this an unbalanced to balanced connection (another thing to study later on) and it is a problem for those trying to make a more ideal connection between cable and dipole. This is why the "balun" was invented, to correct this non-ideal connection.
When I started in ham radio, I strung a wire between some trees with a break in the middle with a piece of plastic holding the two pieces of wire. I fed the center in half wave dipole fashion by stripping the coax back and separating it into a center conductor wire and a shield wire (by twisting the shield braid together) and then soldering these two to the two sides of my dipole. It worked fine.