In my opinion, it isn't the so much eating together it is the actual communication. If you all just sit down and eat and no communication goes on it's not going to really "work". However, if you always have the lines of communication open your children will be less likely to do those things regardless if you eat dinner together or not.
As others have pointed out, that bolded statement is very ignorant. Imagine if your husband left you or got laid off. Was it really your choice to be overworked? Family dynamics are different. As crazy as it sound to you, some mom's do choose to work.

I am one of them. I do not choose to be overworked but I did choose to pursue a career. My children are not overscheduled either. She has swimming from 5:30 - 6:30. Sometimes she eats before swimming. Sometimes we all eat together after swimming. I also have a 3 year old whose bedtime is 7pm. So, that makes eating as a family a bit more difficult. It is important to remember no everyone's family dynamics are the same. I watch as we go out to eat on the weekends. We say grace before the meal and people point at us. There are plenty of people sitting down to eat as a family with no communication going on. They are texting, playing Nintendo DS etc. That is their right. That doesn not mean they don't communicate either.
I'm sure studies show that the more parents are involved the better of the child is. Even with my FT schedule I still find time to attend all school functions, participate in the PTO etc.
BTW, there is a HUGE difference between quality and quantity. Again, just because you all are sitting together doesn't mean it is quality time. I talk to my DD every day on the phone when she gets home from school. I sit down with her and really talk about her day and see if she has any questions about anything that happened throughout the day. I still pack her lunch and make her breakfast in the morning. This morning when I left to drop my DD off at school and for work my DS was still asleep. My DD and myself ate breakfast together. My DH leaves at 6:30am for work. I am certainly not going to wake up the whole family so we can eat breakfast together. My DH has a late meeting tonight so I will be eating with the kids. Technically, we are not eating together as a family.
I am not really seeing an issue here (other than people being judgemental). I haven't read any posts where parents weren't feeding their children.