Um, huh? He was clearly wrong when he said that readied actions cannot interrupt actions. Readied actions can interrupt actions, they can't interrupt their trigger. If the trigger is 'attacks me' then the RA goes right after that attack resolves, but before anything else can happen, including another attack from the same attack action. If you doubt, go read the examples of readied actions on P193 of the PHB and explain how those work if you can't interrupt actions.
I think the term "interrupt actions" may be ambiguous. Does the shield spell "interrupt" an action? If you are hit by an attack (and it actually has to
hit you to trigger the spell), and you cast shield, your AC is increased by five points
including against the trigger. Which may then not hit you. I'd consider that to be "interrupting" an action; it is possible for it to prevent the action from completing.
In 5E, "readied actions" can't do that, so far as I can tell; they go off only
after their trigger is resolved. If you ready a response for "if I am attacked", you get attacked, and the attack is resolved, and
then your response happens.
That said, consider the hypothetical trigger "if someone hits me". If you are hit by someone who has the Extra Attack feature, and you ready a response to run away if they hit you, it seems to me that your response happens between their attack which hits you and any further attacks they might make. Which could prevent them from making those attacks on you.
With the examples they give, where the triggers are movement, it does seem clear that the reaction happens as soon as the other party has moved to the stated location, even if they have additional movement remaining. (Someone could pedantically argue that movement is "not an action", but let's say maybe the enemy first moved towards you, then took the Dash action in order to move further, and had movement remaining in their Dash action.)
But readied actions can't "interrupt" a specific event (like an attack) the way the Shield spell can, and this is a change from the 3.x model, where readied actions were assumed to happen before their triggers (which produced serious chronological problems).