The Defense Intelligence Agency (DIA) is an intelligence agency of the United States federal government, specializing in defense and military intelligence.
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DIA and the Central Intelligence Agency (CIA) are distinct organizations with different functions. DIA focuses on national level defense-military topics, while CIA is concentrated on broader, more general intelligence needs of the President and Cabinet. Additionally, due to DIA's designation as a combat support agency, it has special responsibilities in meeting intelligence requirements specifically for the Secretary of Defense, the Joint Chiefs of Staff, and Combatant Commanders, both in peace and at war
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You will note that the current defector situation appears to violate the obvious scope of the DIA. They have justified such intrusion into normal intelligence areas of responsibility by stating that the CCP has penetrated the CIA, FBI (counter intelligence), State and other civilian diplomatic directed operations. Most likely Dong approached the DIA himself for similar reasons.
My guess is that the FBI is hollering for access to Dong since debriefing defectors is normally their area of responsibility. This case indicates not only how much bureaucratic competition there is between these various agencies responsible for specific intel responsibilities, but also how untrustworthy the CIA and FBI must be viewed by a high level defector.
One of our highest Russian sources, helpful in the Cuban Missile Crisis of 1962, was a GRU Colonel (Russian military intel), Oleg Penkovsky. While his intelligence material was most helpful in resolving the crisis, he was blown too quickly because the KGB had resources in the CIA that alerted them that the U.S. was receiving high grade intel from contact sources within the Kremlin.
It is a shadow world with many snares and (deadly) pitfalls.