Never accused DoD of misreporting J-20.
Though I wonder why they call J-10 and J-11 by F-10 and F-11. By that logic J-20 should = F-20
Also, note they called the JH-7 FB-7. They're probably translating the J to F to stand for fighter in order to clarify their roles. My guess is they left J-20 the way it is because they haven't gotten an official designation from China yet, and it is commonly known as the J-20 in the media. Keep in mind the DoD's audience (mainly Congressman).