I am reading this the same way that you are. If you inflict high damage then the Reflex save is difficult and they take the damage all over again when they remove the harpoon (unless they make the DC 15 Heal check when removing). There is no reason to believe that "precision" damage is any different to that caused by high strength, or Favoured Enemy or anything else.
Thinking about it logically - hit them somewhere vital (ie using precision damage) and it will be more likely to stick in and will cause more damage when you pull it out.
Edit: Following feedback, I have looked at the wording of Sneak Attack (the rogue's attack deals extra damage...), Skirmish (She deals an extra 1d6 points of damage on all attacks...), Favoured Enemy (a +2 bonus on weapon damage rolls...) and strength modifiers for thrown weapons (The wielder applies his or her strength modifier to damage dealt by thrown weapons...). I cannot see a definitive way to separate "precision" additions to damage to other additions to damage, noting that all of this damage would be counted as "piercing" damage.
The original question did not ask whether energy damage (eg from a +1 flaming harpoon) should be added to the Reflex save DC and/or dealt to the victim again when removing a harpoon. RAW it appears that energy damage should be treated the same as any other additional damage (eg Flaming - A flaming weapon deals an extra 1d6 points of fire damage on a successful hit). However, I suggest as a DM that this is not RAI - as noted above, all the non-energy damage is piercing with a logical link to the "lodgement" chance of a harpoon and subsequent additional damage from removing a barbed item.
Overall, the harpoon appears to be a powerful weapon in the hands of a Scout and/or Rogue, especially at low levels. This power level is somewhat offset at higher levels by the wielder being limited to one attack per round, as a full attack action is not possible and as written the harpoon can only be used as a ranged weapon.