Not sure where you heard that, but the first two weeks of Atkins is extremely taxing on the kidneys. The problem comes in when you start adding more carbs - most people fall off the diet at that point, or stop losing. (From my personal experience and trying several times, I could lose exactly 7 pounds on Atkins. Then, no matter how long I stuck with the diet, I couldn't lose any more.) So the urge is to just do the strict meat only portion, and that's where you can really do damage. A friend of mine ended up in the hospital close to kidney failure after a year on strict Atkins. Her docs told her it was the diet. Personally, I don't know how she could stand it for that long.
And..Remember. Normally thin people are not worried about protein or carb intact. It never crosses their thin minds.
I do "fall off the wagon" on occasion (with some pizza or a sandwich) but I try not to let my daily intake of carbs go above 100 g/day. The ADA recommends over 300 grams/carb per day, which is insane but I'm sure many Americans eat even more carbs than that.
If you are getting most of your carbs from grains rather than fruits and veggies, you're getting way too much carbs.
IMO, the low fat diets are far more dangerous than the low carb diets.
Your story is interesting but anecdotal - the point is that there are no documented studies that show a deleterious effect of the Atkins diet. With the chumming that the PETA people have done there is a ton of junk science out there so you may find that when searching.
But the enemy is carbs and fat intake is far less damaging than sugar. Cut out the sugar and so many things fall into place. Atkins was a hero who fought against the madness of substituting sugar for fat in all those "Diet" low-fat products.