Well sometimes from genetics you can venture a good guess as to what is or isn't in a dog's lineage, based on their color or certain hereditary features, but unless someone knew both of this dog's parents there would be no way to know if he does or doesn't have dachshund in him. So I'm not sure why a vet would tell you that.
There's no simple answer when it comes to mixed breeds as a lot of traits can skip generations or are just too recessive to come through. The only way you can really tell is from very costly DNA tests (not the kind you can order online, the kind they perform in genetic or medical research labs), and I'm not sure if those even tell exact breed or just general type. People can guess, but no one can tell you for sure.