I've been watching this forum for a while and decided to register to share a few personal anecdotal observations. By the way, English is not my fist language so please excuse me for not being word-perfect.
I've been skinny most of my childhood. Despite eating ok in elementary school I was just slightly taller than few kids which were really short which meant that 85% of my class were either slightly taller or quite taller than me. Neither of them had a better diet. Some of them were as tall if not even taller than their their parents by 8th grade. All of them ate crappy food while I was eating decently. My diet was consisting of milk and other diary products, beans, potatoes, meat, some fruits and vegetables. I ate almost no refined sugary crap, besides white rice but I combined it with a lot of cheese to make it more palatable. By, the way, did I mentioned that I consumed a lot of diary products? I was eating cheese with every meal and drank milk instead of water most of the time. By 8th grade my height was no more than 170 cm at most and quite likely a little lower than that.
Let me give you another example. My mother's friend kids - a boy and a girl. Our families used to had many trips together and they looked malnourished. They just ate things like biscuits, candy, some bread and pasta. They were pretty poor and the mother neglected them most of the time. When we decided to go to a restaurant one time, the boy had just a small plate with french fries and he puked them shortly after he ate. He just couldn't handle the food! After that his mother was so embarrassed we never went on a trip until 7 years later. They were 14-15 that time, still quite skinny but man, they were quite taller than last time. The girl was shorter than me but not more than 7-8 cm. The boy was like 5 cm taller and I was 18 years old back then. There was a little improvement in nutrition by that time but they still had pretty crappy diet and it was quite obvious that they weren't eating enough. I haven't seen the girl but the boys which is in university now is probably around 188-190 cm when I saw him recently. Still skinny as a rake. I don't try to claim that nutrition is not important in regards to height but it can only help in reaching the predetermined height by birth. By the way - his father is also tall, the mother is taller than average for female in my country. It's not a big surprise they are tall as well.
Another personal anecdote is from my family. My two female cousins were raised in quite turbulent environment. They had the same crappy diet - bread, cheap canned food, a lot of sugary crap. They were both neglected in their early years. During a particular period of time their parents left them and went to a different country to work so my grandfather was forced to take care of them while they were working abroad. Even my mother and father bought them food to get by. The bigger one was even hit by a car and spend some time in a hospital. I learned years later that they were abused by their mother and they saw their mother abusing their father as well. Truly terrible conditions. When they were 12-13 and 7-8 years old respectively their parents took them in Italy where they managed to rent a small apartment. They were still struggling there. When they decided to visit us few years later the older one was a head taller than I last remembered her. Initially, I even thought she was my height. When I asked her how tall she was she told me 174 cm. This is almost 10 cm above the average in Bulgaria. Her sister was just 160 cm which is 4-5 below average. Their parents are: father 174 cm; mother 160 cm. As you can see the bigger sister was 14 cm taller than her mother and the same height as her father and the little one the same height as her mother.
Again, despite awful upbringing, one of them turned out taller than expected and the other one pretty much as expected.
Now two different examples:
A client of mine who is ~179 cm with father 185-186 cm. His mother is not short - 164 cm. Perfectly normal height but his predicted one is at least 181. He was raised in wealthy family, well fed, played sports, got good education. Contrary, his tall father was raised in poverty, smoked from young age and yet, reached quite decent height.
My brother's friend is around 170 cm, his father is pretty much the same height if not a little taller, mother, a little on the sorter side but close to average. The same guy was eating like a king every day. Never stressed, quite happy and funny guy. Yet, never surpassed his father despite raised in excellent conditions. He is quite successful despite his relatively short stature. He wasn't interested in chasing girls anyway and invested his time in studying and enjoying life. He now works as a manager for a pretty big company.
What all this goes to show? Most likely not much since these are just personal observations. However my explanation is simple. Stressing on such things is not worth the time. You can't tell how things will turn out if you did things differently. Most likely everything will be pretty much the same or an inch at most but no one can tell for sure. Some people will grow tall no matter what and others will be short or average despite living under perfect conditions.