Navigator Role ability
The rules list four actions that a player can take on their turn:


  
  Move
  Shore Up
  Give a Treasure Card 
  Capture a Treasure
  


Note that Move is an action and Shore Up is a different action.

The Navigator's card text says the following:


  Move another player up to 2 adjacent tiles for 1 action.


Since shoring up (or giving a treasure card, or capturing a treasure, or using a special ability that requires an action) is distinct from movement, the Navigator is only permitted to make them do the Move action. I imagine it would say something like "Have another player take 1 action for 1 of your actions" or something if it were allowed.

On the plus side, Navigators are useful for helping other players get in position, and they can move a character 2 tiles instead of the usual 1 that they would be doing on their turn.