At the beginning of Terminator, Reece (the guy who was sent back in time to protect Sarah Connor) told her he could not carry any weapons or other non living material. Asked how the Terminator could use the machine he answered that the Terminator was covered by living tissue.

But in both Terminator 2: Judgement Day and Terminator 3: Rise of the machines the T-1000 and TX could also use the time-travel machine. Both models consist of liquid metal, in T3 it is a solid skeleton under liquid metal as you can clearly see in some scenes.

So how could pure metal be alive and thus use the time-travel?