That is correct. That is also why fuel mixture changes as the main tank empties. A Uniflow setup will cure that but lets not get into that.
The fuel mixture change we are talking about occurs at the very end of the main tank run. At this point the mixture will be leaner than at the start of the flight partly because of fishpucks observation. Now as the main goes completely empty, the fuel doesn't have to travel from the main tank clunk through the fuel line to the header anymore. Essentially you are now looking at a small, completely full tank much closer to the engine with a big, long muffler pressure line. So the mixture will go rich.

Fritz