From your title and question can I assume that, since they're arborvitae and you specifically say BETWEEN them, that it's a hedge?
If so, then - depending how big these blocks are - there is more than enough space around each tree for the roots to grow unhindered by a hard surface and water will creep underneath them too to allow for moisture absorption, and yes retention (lift a rock or slab and it's always moister underneath, hence why slugs love hiding there...) so in that regard he's right
Besides, when laid on top, these blocks don't really interfere with root growth since they grow underneath. I don't know in the case of arborvitae, but there are plenty of species of trees that are planted in a square a metre space surrounded by hard surfaces such as in cities. Trees adapted to these conditions do just fine nonetheless or even lift the entire pavement and road.
But why concrete blocks? They're ugly, heavy and better suited for other purposes. A coarse organic mulch laid thick enough will just as easily prevent weeds while allowing the better aeration, water infiltration/retention and soil building. It's much more pleasing to the eye too, albeit not forever lasting.