Simply not true. Here is an excerpt from the US Embassy in Ukraine website:
"The U.S. Department of Defense’s Biological Threat Reduction Program collaborates with partner countries to counter the threat of outbreaks (deliberate, accidental, or natural) of the world’s most dangerous infectious diseases. ... The Biological Threat Reduction Program’s priorities in Ukraine are to consolidate and secure pathogens and toxins of security concern and to continue to ensure Ukraine can detect and report outbreaks caused by dangerous pathogens before they pose security or stability threats.
"Current executive agents of the Biological Threat Reduction Program in Ukraine are the Ministry of Health, the State Service of Ukraine for Food Safety and Consumer Protection, the National Academy of Agrarian Sciences, and the Ministry of Defense."
BTW, the BBC is not a credible source, as it is a state-funded and state-run propaganda outlet, much like the old Pravda in the USSR. It is by NO MEANS an independent news source.