You aren't going to do that on a plant based diet. At least I haven't seen that yet. They are right that vegan diets usually recommend eating real foods, i.e. foods that are not processed or minimally processed, and so do low carb diets. But they are really two different diets that do different things.
And keto diets are very different than low carb diets that don't limit carbs as much. But, like I said, it's possible to do well on diets of all different kinds. My wife eats a diet recommended by a dietician who specializes in diabetes. She's has type 2 diabetes. The diet I eat can actually be harmful to her due to the medication that she takes to control her diabetes. She needs about 100 carbs a day to maintain the proper balance with her medication. If she consistently goes too low it can induce a toxic state in her body called ketoacidosis.
So it all depends on what you need and your preferences. Both of us appear to be saying that. But vegan diets and keto diets do not produce the same results. You might lose weight on both, but internally there are big differences.
Also, on the keto diet it's not necessary to exercise to lose weight while still eating well. That might sound counter-intuitive, but there are many examples of people who consistently lose weight on the keto diet without upping their physical activity.
The keto diet is not for everyone, but it works well for a lot of people, and it is working well for me. Vegan diets are probably not superior for health as has been advertised for a long time. The opposite might be true. But they are good for people who have ethical problems with eating animal products.