This makes a lot of sense to me. I suppose it's all in the wording. Even IF movement was an action (which the above posters have convinced me it is not, thank you for the explanations,) just stating "I'll shoot as soon as he moves 5ft closer to me" would be enough to shoot before he reaches you, as your Ready action would go off after he moves that 5ft. So this is all good to know.
I wonder if the biggest reason behind the wording in the DMG is to give a bit of a boon to spellcasters when they cast a spell?
By making your Readied action occur after the triggering Action, you can no longer shoot a caster as he casts a spell, potentially ruining it. This is important to know, as there could be times a DM (one playing particularly savvy foes), might have five archers Ready actions to shoot the spellcaster if he casts a spell, which would force five separate Concentration checks. Now, the caster would complete the spell, then five arrows would come his way. Equally scary, but perhaps less frustrating?