But this is not the meaning assigned in the case of Trump. The conspiracy theory is that he is "owned" in the sense of having some secret that can be exploited by Russia.
There is a belief that he is an agent turned by kopromat, but the view that he is an asset is broader (since assets include agents, people using the “asset” description may hold to the stronger or weaker form, and often, in practice, believe that is af least the weaker form and possibly the stronger.)