The majority of my boxes are double walled. Some have more ink than others. No idea what is in the ink, or the glue. We know where glue comes from, and I would think that it would break down, but I'm less worried about the glue and ink than I am chemicals. Who knows? Maybe the ink and glue is actually worse. Either way, I'm not going to worry about it. I've had great success in the past doing things this way, and I know it works. I've never lost a plant where I've used this method, so I have to think that the ink and glue is safe. But, I've never planted veggies in a bed that I've done this in. Since I'll be planted some veggies in this area before the grass is probably completely dead, I'm still not worried about it. I'll remove that section of grass by hand, and will mulch. The cardboard probably won't be broken down by then, so if there is anything harmful, which I doubt, it will be removed anyway.
I think our puppy would be dead if the ink and glue was harmful. He's been chewing on the boxes for a week now, and still going strong.