probably two things - a) using voice activation instead of push to talk, and b) the sound card has a feature to use as input "what you hear" rather than microphone. My nVidia board's built in sound card has that thing, and if you check that in addition to the mic input, it will feed everything you hear back into Teamspeak.
However, if you can hear other stuff from the room he's in, then he's just not using a headset. Also, push to talk - that's the ONLY way to go when you have speakers
Bad things don't happen to you because of bad luck. They happen because you are a dumbass.