Aunt Mary's Double Irish Chain

I took a DNA test last year, expecting it to confirm what I already knew. My mother’s father came from Munich in 1924. My mother’s mother was a Mayflower descendant who claimed there were Indians in our family tree. My father’s father was the product of Mormon pioneers from England. My father’s mother could trace her paternal line back to a soldier in the Revolutionary War, and her mom was from Amsterdam. So I was sure my DNA profile would show 63% English, 25% German, and 12% Danish with little Native American for good measure. As it turns out, I’m 38% Irish and 22% English. Only 17% of my DNA comes from Western Europe (so my Bavarian grandfather or my Danish great-grandmother must have really come from someplace else). Apparently I have a great-great-grandparent from Italy or Greece, one from Poland or Slovakia, and one from Finland or Russia. Alas, I have no Indian blood.