My thought
Obama replaced ALL of the computers in WH. I suspect more than one can be controlled to listen in from elsewhere.
Like the voting machines that can be controlled by cell phone (actually witnessed before it was decertified in our state) the new machines are deviously used.
It would not be for Obama to replace computers.
Networked(voip) desk phones can be easily hacked to listen to what is going on in the room - especially if you installed the system.
Hopefully they took steps to preclude that. Another potential issue would be if they’re using any voice-controlled apps or features like Windows 10 Cortana. “Siri, find me the leaker.” “The leaker is Ben Rhodes. . .”