While I'm suspicious of the idea, a growing Earth doesn't sound that hard to conceptualize to me. IF the Earth grows, perhaps it's not the mass that is changing but rather its volume and density. Let's say the core of the Earth became less dense for some reason, couldn't the Earth expand without necessarily gaining mass?
I suppose it could but I don't think it has to. Meteorites have been raining down on the planet for four billion years and have provided something like 3 times ten to the fifteenth tons of mass. Sounds like a big number but it is over a very long time. A growing Earth would be a very slow process.