Addictions are unhealthy dependencies. When we drink alcohol we are not always addicted. When we go for a walk we are almost never addicted. So there is a variety to everything we do in ways good and bad.
Zen Buddhism has helping us with our breathing 'addictions' as one of its main goals. So yes many people breathe in an unhealthy way. Whether all of us as a species do breathe unhealthily is debatable. Some might say being alive is addictive.
The assertion is bizarro similar to Judaism central tenet. All men (and women) are fallen beings. It's similar because if we all are addicted to breathing as OP claims we all have a kind of metaphorical thorn in our sides. As for general fallen natures as such? Christianity declares this is reversible.
On the other hand Taoism which is a precursor, along with Buddhism itself, to Zen Buddhism has 'older' ideas. There is an essence that is unknowable. Humans have lost access to this essence and no amount of meditation will revive the essence in us. So from this perspective those who agree might be considered Daoist.
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