Yes, true, especially if you live in a hot place or like to leave ur phone in "closed" places such as your pocket or purse.
If you live in a hot place or like to use your phone while it charges it is always a great idea to remove it from the case.
This is not a problem, in fact it is common with every single gadget. If you use it too much it gets hot. Now imagine having something that can get hot covered with an extra layer of plastic/rubber etc? It will definietly overheat.
Pay extra attention if you are a heavy user and use impact cases (those with layers of plastic and rubber together).
If your phone overheats often you will be "frying" its components inside. The same goes for the engine of a car, if it overheats you will have issues.
So the answer is yes, you can damage your phone if using a case the wrong way :)