This is partly a myth and partly due to the physical size of the bass.
Some people (even professional musicians) believe that low frequency sound waves "need room to develop". That's completely false. One thing that can happen with low frequency waves is they are more likely to form standing wave patterns inside smaller rooms. Those patterns will create spots where the overlapping waves reinforce or cancel each other out (anti-nodes and nodes, respectively). Sometimes a node is very close to the instrument and moving away from the instrument towards an anti-node makes the instrument sound louder. But in an open field or a large enough hall, the bass will sound loudest when you are right next to it.
The one way in which this is not a myth is that the resonating body of the bass is very large, and different aspects of the sound of the bass can resonate from different parts of the body. That means when you are very close to a bass, certain sound components may be much louder than others, and you might not be able to discern the quieter components (which are quieter because they are coming from the other side of the bass).
When you move away from the bass, all the sound components mix together appropriately and you can hear each aspect of the sound at its appropriate relative volume.
Also note that bass players have their ears in one of the worst possible places to hear their own instrument! The bass radiates a lot more from its face than from the fingerboard. Bass players will hear a lot more fingerboard noises and the vibrations of the neck more directly. They may also have some amount of bone conduction of vibration from the neck of the bass, and bone conduction distorts the sound a lot.
Without a space that effectively reflects the sound back to the player's ears, playing the bass is a bit of an act of faith. So the bass player in question is completely correct to believe that if they could only stand in front of their bass about 5 - 10 feet away (because of the angle of the face of the bass being pointed slightly upwards), they would hear it most clearly. That's more of a position thing than a distance thing. If a bass player could remotely locate their ears the exact same distance from the f-holes as usual but directly in front of the bass instead of up near the scroll, they would find it quite loud and full sounding.