It said it in a different way, by speaking of the effects of the sound waves themselves on the density of the substance through which they travel. By reducing the density of the substance above in a gravity field, the sound wave induces its own (slight) upward travel. This must be something very slight, or we’d already know about it in standard acoustics.
What you said: By reducing the density of the substance above in a gravity field, the sound wave induces its own (slight) upward travel.
This reminds me of some of the stuff discussed in controversial TV shows about ancient astronauts and such. Basically, that heavy stones and objects were moved in the distant past by use of sound energy to reduce the density of objects and lift them upwards in a gravitational field. Various devices used to generate particular vibratory sounds to lift heavy objects. Most people say it's BS, but we don't know what we don't know.
If you're talking about the Bernouli effect, then a 747 has negative mass--according to the article. It does not.
With sound traveling long distances, the downward curve of the earth is going to have much more of an effect I’d bet.