Come again? Starbucks products sold at Dollar Tree are as real as those sold in other food stores. The Starbucks grocery business is owned by Nestle.
I mean, it's likely not the same as what you'd buy in a Starbuck in the USA. It's was probably packaged for Mexico or someplace, didn't sell, and the overstock was sold to Dollar Tree.
They did this with Colgate Toothpaste a while back. It was a minor scandal. It was real Colgate, but not the USA formula. It was not ADA approved and didn't have the same flouride content.
Hence "Starbucks brand" (real in the same sense that Versace eyewear is actually made by Luxxotica)