Half-and-half (as in half-truth)

Today, my wife and I were shopping in Wally's World. She wanted to find some non-dairy creamer to use in her coffee in the morning. However, when she picked up the container to read what's in it, she found, to her great dismay, that each brand had the same first ingredient:
MILK.
Hold on there, Bessie! Isn't the definition of dairy any product made from MILK or CREAM? How then can they market their product(s) as non-dairy?

Somebody get Oliver Stone on the phone for me. I smell a conspiracy!