This statement is no exaggeration, if you push in an upright relaxed body posture and use a pushing method with less impact on your bones. So here is some further explanation:
One fundamental advantage of pushing is, that you can use the skateboard as a tool to carry your feet. When running, the impact for the feet in the moment of touching the ground can be quite strong. If your heels are the first part of your feet that comes into contact with the ground or if you have a pronation when running, you will most probably damage your joints sooner or later. When pushing, the impact happens in the moment you are putting your foot down to the ground to propel yourself forward. But since you are standing with one foot on the board while already rolling forward, you have more time and control to prepare your step to the ground. This way it becomes possible to minimize the impact when putting your foot down by first moving it into a preferably low position above the ground before making a smooth step. You don‘t have this advantage when running, since running means to lift your back foot off the ground already before the front foot will again be landing on it. Otherwise you wouldn‘t be running but walking. When running you are actually performing a constant series of jumps. Because of this it is not possible to control the power of the impact in the same way like when pushing a skateboard.
Regarding the impact for your joints and bones, pushing also has another advantage: When running both of your feet are constantly engaged. But when pushing, you can keep one foot on top of the deck for some period of time and this way remove the stress resulting from the continuous stepping against the ground. This is especially true for the method of ChiPushing, because the leg on top of the board is completely relieved, pushing the board forward in a relaxed way without exerting downward pressure, as all of the body weight is carried by the leg touching the ground. If you switch sides to push with the other foot, the leg previously stepping against the ground will then take over the position on top of the board and get some relieve. Skogging (skate-jogging by alternately using both legs) is an important part to reduce stress for the body when pushing.
Finally another important ergonomical aspect that makes pushing a skateboard a very natural and one of the least stressful ways to travel, is described by the fitness and mobility coach Dr. Kelly Starrett in his book „Sitting is the new smoking“. He writes about the health advantages of passive standing in contrast to our modern lifestyle of too much sitting for long periods of time. Although he doesn’t mention skateboarding in his book, the principle he describes can be very well transferred to the act of pushing: When standing for longer periods of time, we like to lift one of our legs on top of an obstacle to bring it into a slightly higher position, because the resulting change in the area of the pelvis will help to take passive stress from our lower back and spine and allow us to stand for longer without feeling fatigue. Dr. Starrett takes the example of bars in pubs where people are drinking in a standing position. Some of these bars have poles at the front. The guests can rest their feet on these poles, which makes it easier for them to stand longer and to consume more drinks. It is easy to see the similarity to the body posture when pushing. Of course I don’t want to say, that all skaters are heavy drinkers, but the foot on top of the board is just the same in a higher position than the other one. In ChiPushing we use our foot standing on the deck to move it forward. This movement with the leg standing slightly higher on top of the board additionally helps to bring the pelvis into a favorable and stable position, that makes it easier to adjust the spine and to reduce stress in the back. Considering this we can see, that dropped decks are not necessarily better in every aspect of pushing.
When done correctly, pushing a skateboard is a simple yet efficient way of moving around, allowing us to transfer the same relieving principle that reduces stress when standing for longer periods of time, to create an efficient and least stressful way for our body to travel longer distances.