Learning the Vines tutorial, page 18: is the explanation of movement correct?

No. The second Movement section on that page says that you move both the battleborn and dispatch 2 hexes towards the grovetender fortress gate, and that while the battleborn had another movement option, it would have ended on a hex within the shrubbery's range, which you want to avoid. The reasoning given, that you want to avoid being in the shrubbery's range, is incorrect, because the shrubbery has no attack upgrades so cannot attack your units regardless. The battleborn also cannot successfully attack the shrubbery, because the battleborn only deals 1 damage and the shrubbery has a fortification upgrade on the bottom so requires 2 damage to be dealt. So, because there is no benefit in ending movement beside the spire, the tutorial opts for the battleborn to end its movement on the hex that has it making as much progress towards the fortress as possible.