The first statement is correct. The second is wrong. It makes the unwarranted assumption that a prior ancestor of both chimps and humans is a prior ancestor to all apes.
You're right. This assumption is not only unwarranted, but contradicted by the molecular data we have. Humans and chimps have viral introns in their DNA that no other primates share.
Human and Chimpanzee Functional DNA Shows They Are More Similar To Each Other Than Either Is To Other Apes. (Long PDF file.)
Humans and chimps are far more related to each other than either is to the orangutan. Humans and chimps are very close. When Humans, chimps, gorillas, and orangutans are compared, one species stands out as far different from the others. That's the oranguatan.