While most of what you say is correct, hence removed from the quote, this statement is clearly INCORRECT. For example, arriving to FRA and transiting to HAM/TXL/MUC is seamless. You do customs at the last airport, you do only immigration to Schengen in FRA. As a matter of the fact, this applies to the whole Schengen. You do immigration at the first point of entry, but customs at the final destination. Same applies if you fly to (e.g.) NCE via CDG..