There’s little chance that the statement is true. Chickens kept in a backyard can live on bugs and kitchen scraps and there’s no delivery cost for eggs or eventual meat.
This is not how the overwhelming majority of chickens live - they live in high intensity farm operations in horrible conditions
If all the meat you eat is from chicken raised in your backyard , that's environmentally perfect.
In the US per capita chicken consumption is 100 pounds per year.
That is not how most of the chicken is raised (over 70 billions are slaughtered per year).
Back of the envelope, for a family of 4 eating US quantities of chicken... you need to be slaughtering ~100 chickens per year. In a homesteading setting it usually takes a chicken about 12 weeks to reach slaughter weight, so you need to be raising a minimum of 25 at any time.
That's a pretty substantial backyard operation.
how big is your backyard?
A negligible fraction of chicken production is backyard operations. Any quote talking about chicken production is referencing how they are actually produced, which is generally huge industrialized farms (often hundreds of thousands to millions of birds a year).