Everything that you can eat or is a discard from what you eat (vegetable/fruit) can go into the compost heap. It's what worms eat. And it's way more than OK so long as it doesn't make the heap so wet it goes anaerobic.
The important parts are getting the CN ratio correct so that bacteria thrive, and having the contents just moist enough that aerobic bacteria and fungi thrive. The bacteria require nitrogen as part of their lifecycle, and the fungi break down cellulose and lignins (woody high carbon (brown matter)) so that the bacteria can then process it.
All organic matter from green rose clippings to tea bags is grist for the heap, once you have it properly going with a healthy bacterial/fungal environment, it will break down anything, including accidental included small pieces of ground cloth you originally put down for weed control.
Your major worries should be not getting unwanted seeds into the heap, grass seeds, spearmint seeds, dandelion seeds and anything else you don't want to propagate, so all input materials need to be harvested before the seeds become viable. Now there's something that can be not ok. Compost cucumbers and tomatillos can be the most healthy unplanned plantings you will produce.
If the heap is in contact with the soil, fruit/vegetable matter is great for attracting native earthworms which will then go on to consume all leaf matter and grind it into rich vermicompost.
So I fired up the TED talk and listened to it...
Sorry, composting doesn't start in fall with leaves or in spring when you start dealing with vegetable food waste. It's a year around process.
True, vegetable kitchen waste only will create a horrible mess, unless you're using the Japanese Bokashi fermentation method.
Sorry, wrong on the nitrogen content, fruiting plants move all their nutrients into the fruit and seeds in order to pass it on to the next generation.
Yes I agree, leaves are wasted by most people, and yes they have to be shredded if you want them to compost quickly. A lawnmower can do the shredding just as well as anything.
Worm bins? Never have needed them, that's what your compost heap becomes when you add kitchen waste.
What're Karma points worth, I do it for enlightened selfish reasons. I don't have to pay for hauling it away to be buried, and the garden food tastes so good! We probably agree wholeheartedly there.
Also, there are many composting methods. You don't even need a bin. And the easiest for kitchen waste is potholing. Dig a hole in between your intended plants, bury it and let the worms eat it. Plants will grow feeder roots into the remains.