This is true. I am mixed white.latin.black and have had many people throughout my life try to identify me as only one, either latin, white, or black, and I'm very much like, "No, I'm all three!"
I had a friend who was Black and Mexican and she's like I'm Black! I'm like no your mixed, lol. But I can see how its annoying for both of us.
People should be able to claim what they want. For me I don't identify with any one of my sides more than any other so I feel weird claiming only 1 or 2. I think my friend grew up with her Black family more so feels more comfortable identifying as such.