They also say the Anunnaki are our parents, too. Were they involved in creating the human race, as opposed to just interbreeding with human females to start a separate hybrid bloodline?

Here, too, we used many components from the Anunnaki to create the divine human because they were good ideas and time tested and of value, but they did not create you. They, however, have altered you in significant ways and in that sense have become responsible for who you are today to a significant degree because your degraded status owes to them, so in a sense they have parented a kind of aberration of the divine human, severely attenuated with a number of limitations compared to its native configuration and of course, in addition, they have interbred directly to create a bloodline and that has further increased their influence on humanity, at least genetically.