Not read all the replies, but here's my tuppence worth.
My DD would have been ravenous if made to wait that long between meals with no snacks. Infact she would have been a nightmare to be around as a hungry child is not a happy child.
I also think that separating adults and childrens meal times (unless due to work commitments etc) is a bad example to set. Here if we are all in, we all eat together around 530-6.
A normal day for my 7yo DD would look like this.
Breakfast around 730 - cereal, toast and chocolate spread, glass of fruit juice and possibly some fruit too.
Lunch around 1230 - if at school a hot meal, if at home then maybe a toastie, or beans on toast, or a wrap, usually with salady bits and some crisps on the side. A biscuit and a drink of juice.
Dinner around 530 - a proper hot meal, tonight was a roast chicken with all the trimmings, and a chocolate mouse.
She also had a packet of popcorn today between lunch and dinner.
Supper - pancakes, or toast, or a dairylea dunker or similar! With a drink.
My DD is very tall for her age (wearing age 11 clothes at 7yo). But is perfectly in proportion, there is not a pick of fat on her. She dances twice a week and swims once a week along with other activities and playing out every day.
No food is bad food here, everything in moderation is the way we work. Your relationship with food sounds difficult to me, and unhealthy.
So in conclusion YABU.