While that piece of junk is technically right that "processing food" is an expression too wide to base any descision on (it DOES range from cooking or canning to adding 99% artificial ingredients and still call it food) it completly leaves out the problematic processes. The basic claim is that just because cooking food is also a kind of process, all processing done to food is harmless. Well yeah. sometimes my life would be easier if I was dumb enough to believe such BS.
But what you mentioned is still a good rule of thumb. The more of the "food processing" (from cutting to cooking) is done in your own kitchen, the better control YOU have of the whole process. And the more control you have, the less likely it becomes that you're doing something that would only benefit the manufacturer by reducing quality for the sake of profits. If you do, well, then it's quite stupid, but your own descision.
The less complex processes a food item has gone through, the easier it is for the layman to see if it is a quality enhancing or a profit enhancing process.
Likewise, the "if you can't spell it, don't eat it" is also a good rule of thumb to avoid unneccessary additives. And that even holds through for your Vitamin C example. If it is listed as an additive, it has usually NOT beed added because of its benefits as a vitamin, but as a preservative. And even as it is essential (no doubt about that) you can get more than enough by eating easy to spell food as "fruit" or "bell pepper"
If you really have to take additional vitamin suplements, that's a sign of malnutrition (or medical condition) and you should change your basic diet.