Mixed? Me? No! Well...Kind of. Technically. Should I care?

Racialicious posted something today that brought up a topic I struggle with from time to time, mostly whenever I'm filling out some form that asks about my racial identity and asks me to select all that apply. 

I am a black person. I prefer to identify myself as a Black American, though I can accept multigenerational African-American (Imani Perry term), and will respond to African-American more broadly. I don't like the term African-American because I don't have very strong ties with Africa culturally or otherwise. I am somewhat Afrocentric, with my style of jewelry and sometimes clothing, and my hair to a degree (but that wasn't the original intent), and how I try to celebrate Kwanzaa. I think I prefer to think of it as ethnocentric. But another part of my reasons for disliking the term African-American is the simple fact that some of my foremothers and forefathers [yo, why is forefathers a word as recognized by the internet and foremothers isn't? Sexist and rude.] were not of African descent; their inclusion in my family tree was done through a mixture of choice and domination. This means that technically, despite the fact that I and my parents and my mother's mother all identify as black people, I am an individual of mixed race. Is this an identity I should embrace? I am a black person [with bits of German, Portuguese, Native American, mysterious-probably-white-Canadian, AND NOBODY KNOWS OR CAN EVER KNOW WHAT ELSE]. It is an inherent part of the process of having descended from a people who were not regarded as people. Am I denying the other parts of my ancestry by claiming only my blackness? Is this doing my ancestors (moreso the ones in my family tree due to love) a disservice? Or does claiming a black identity automatically include all the various mixings that produced black people, because to be a multigenerational African-American means to have been mixed? I don't ever check anything but Black/African-American on forms that say to select all that apply, because I don't identify as anything else. Should I?