Building a shipyard during canal phase
[a level 1 shipyard] has no materials needed to be shipped


I believe you've got that part wrong: A shipyard does require coal (look at the brown square at the bottom-right corner of the tile), so a city must be connected to a source of coal through canals or rails before you can build a shipyard there.
http://www.boardgamegeek.com/image/307212/brass

Barrow-in-Furness and Birkenhead may only have rail links (notice that there's no blue line) to the rest of the map, from where coal may come.

Therefore during the canal phase, the only possible shipyard location is Liverpool as you can build a canal link to Wiggan or other potential coal sources; but there is no such potential canal link out of Barrow-in-Furness or Birkenhead.