The argument was that although it's true that your time will pass more slowly than time on Earth while you're coasting, you also clearly have to do a lot of accelerating, and acceleration itself also has an effect on the apparent passage of time in your reference frame -- and in this scenario, where you start and end in Earth's reference frame, that effect cancels out the effect of velocity (perhaps even more than cancels it out; I don't recall).
Does anyone here know if this is true?