That may be true, but the parent is tasked with determining what is appropriate for the child. Each child is different - hence the word, 'parenting'.
Just because they come out of it without being scarred for life, it doesnt mean the movies you cite should be offered freely without limits to children. People put too much weight on ratings, as if they somehow free the parent from the responsibilty of checking the content which is why props to the OP for tackling the subect and doing the rewatch. If they think their kid can handle it - go for it in a controlled way.
I watched Robocop when I was 9 sneakily at a friends house and did just fine - but Im glad my parents didnt give me such a free reign that my mates friends parents did (who didnt give two shits what he watched - it wasnt the movies but such an careless parental attitude that contributed in leading that mate to go on to be a nasty piece of work)
Good post. I think I ended up watching The Matrix in cinemas when I was 9. As was stated above, The Matrix was rated PG-13 equivalent in Australia so it wasn't a huge deal but my parents loosely enforced ratings rules in our house. When I saw some horrible shit on screen when I was young, it didn't scar me for life, but some stuff certainly freaked me out at the time. Sometimes I would go to bed worrying about murderers breaking in and doing the same horrible shit I just saw on screen earlier that night.
In regards to OP's question, The Matrix is a strange one I think. It's not really as violent, doesn't have as much swearing (no f-bombs at all I don't think), or as much sexual imagery (one scene in the sequel) as a regular R-rated film. But at the same time, it is a bit harder than a PG-13 you feel. Blood is there when it needs to be there. The characters freely say 'shit,' which is, as far as I know, not so prominent in a regular PG-13 film. I love this kind of filmmaking. Usually, the team will either try to squeeze a film into the PG-13 slot, and as a result it always feels a little bit artificial - The Dark Knight's lack of blood entirely for example. That, or they say 'fuck it - It's gonna be R. May as well go balls to the walls and make it a selling point. Every actor, ramp up on the f-strikes. Every action scene needs blood pouring from the arteries.'
The Matrix just tells the story it wants to tell. If violence is necessary here, it'll throw it in freely but it won't be a staple of every action scene. Most of the martial arts scenes are blood free - delicately stylized appropriate to the world of The Matrix. But over the course of the series, you'll see charred arms, skewered bodies, torture, burnt/singed eyes by sparky-hot-cable and knife stabs. And it's all quite graphic but it's all there for the story. I would imagine having a studio allowing that amount of freedom would feel quite liberating.
If I could make this post just a tad longer, I suppose I'd also like to bring up the themes and tone too. I think the thing that ultimately makes The Matrix fine to show to a younger audience is that it's, in essence, a good vs. evil story. There are heroes we can root for who ultimately prevail against the forces of evil. There are casualties along the way, but that's what always got me to sleep at night when I was younger - the notion that good is out there and will stop evil. More mature R-rated films with more mature themes would have scared the shit out of me. Ones where the protagonist is a shade of evil and the right things don't always end up happening. Or there are psychopaths who get humanised and explored. I feel like there isn't really enough weight put on this by classification boards as there probably should be.
But The Matrix is certainly heavier thematically than a more typical PG-13 film like Star Wars. It does deal with strange and confronting ideas. It's a pretty shocking setting and premise and there's no easy way out. The idea that your whole life has effectively been a lie and you're being monitored constantly to conform is a bit terrifying. The imagery of being possessed without knowing or agreeing to is pretty scary. And then you might be dead by the time you get your body back. I always felt sorry for the homeless guy just minding his own business who got taken over by Smith and ended up being squashed by the train.