I hope you don't mind if I answer. My one time being late to an ADR was due to an accident on the road (my family was going by taxi to the Poly). At the Kona Cafe there was a line up of people trying to check in. The CM was making no bones about people who were late, and even told us we were lucky that the monorail was having issues, so they were told to accommodate people who were late. And that otherwise we wouldn't have been seated.
Disney will try to err on making the guest happy whenever they can. But I take huge exception to someone claiming anything is fine all of the time. If push comes to shove Disney can tell you you missed your ADR slot. They won't do it if they can avoid it, but to claim they never do it is flat out wrong. It is never ok to tell someone something that can cause such headaches with their vacation. It is fine and dandy to say Disney sent you an e-mail, but who will be there to pick up the pieces if something else happens during your trip? Saying "so and so on the Dis got an e-mail and they say you always seat people who are 15 minutes late!" won't help much.
Actually I'm sure if you asked to speak to a manager and showed them the email that they would probably relent... I can't imagine the not at that point.
That said, who wants that hassle, headache and confrontation on their vacation? It's a good policy to try to be there 10-15 minutes early for your ADR and sometimes stuff happens and in general they will accommodate you when it does. It's in general a bad policy to PLAN to be late, but I also would not live in fear that if you are late because of something that is out of your control that Disney is going to take a hard line on it... I think chances are very very low of that actually happening and I would not add that level of stress to my vacation worrying about it.
Though honestly a good friend of mine had a completely HORRIBLE experience with the manager at Brown Derby so I know anything is possible, but it is just NOT typical Disney at all.
She showed up early for lunch with an imagineer after being thrilled to score a last minute ADR on her solo trip... her one weekend of the year break from her two children, both autistic. It was to be the highlight of her trip and she got there nice and early and kept being told "not yet" until a half hour after it was supposed to start and several trips to the podium and kept being told "not yet." Well it DID start and she missed the first half hour. She was understandably upset and was told she could join it late or forfeit the price in full. Over THEIR mistake. She asked for a partial refund to join it in progress for the course and time she missed and the manager said no. She burst into tears and the manager said or did nothing, she left crying and was charged for a no-show. I was horrified when I heard but apparently stuff like this does happen.
She did complain after the fact and got a refund but it ruined her entire day until the CM at her resort gave her some vouchers for a free meal elsewhere when she burst into tears again at the counter. I honestly could not believe a manager would treat someone like that. So I guess your story doesn't surprise me... but it also doesn't make that kind of treatment right at all.
Honestly I think that cm was downright nasty. You told her there was an accident and you were stuck in traffic and she still gave you a lecture about how she wished she could have denied you but was told not to because of a monorail incident? That is not someone who needs to be a hostess IMO. If they were told to accommodate people who were late she should have done so without the lecture about it and making people feel bad, or that they were lucky just to get a seat. There is nothing remotely magical about that and I'd be saying something to a manager if someone started wagging their finger at me like that! I'm sorry but that is terrible customer service and not the least bit appropriate to deal with a customer in that way. Either seat them, or don't, but don't chastise them. It's not your place.
But planning to show up late is nothing short of rude. don't do it. And if you miss your ADR then you deserve it. I think most miss it due to stuff out of their direct control so Disney will mostly err on the side of making magic. And of course you can always get someone with a bug up their butt about it. But if I had a legit excuse I'd talk to a manager upon being turned away. I've never had it happen or even threatened even when quite late. No one even asked me why. I checked in and was seated.