I'm trying to understand how a colonist career skill selection works. The basic colonist gets a variety of knowledge skills for his career (core worlds, education, lore). But the Doctor and Politico specializations also "adds" one of those same career skills.

Is this a typo? Or is it meant to allow a colonist to get two free ranks of a knowledge skill if he so chooses to?

Yeah, many Specializations have skills that match one or more of their career skills. This is intentional, and as you say allows such a character to double up on free skill ranks (max 2) at character creation.

Is this a typo? Or is it meant to allow a colonist to get two free ranks of a knowledge skill if he so chooses to?

Nope, it's not a typo, but rather a deliberate design choice to let a PC that starts out with a given career/spec combo to be really good at a certain thing (such as the Colonist/Politico being able to stack Charm and Deception) or to branch out into several notable skills (such as the Scholar having at least one rank in plenty of Knowledge skills to start with).

Also when another career chooses the specialisation, they get the correct career skills as appropriate.

Also when another career chooses the specialisation, they get the correct career skills as appropriate.

Just to clarify; those skills become career skills, the character doesn't actually gain ranks in any of them unless they chose to spend the XP to do so.