At worst: Option 2 - You can replace the bad boards. Option 3 - You can either refinish the floor (IF there's enough 'wood' to sand.) Option 4 - You can replace the entire floor. SO, attempting to bleach-out the stain is OK to try.
Option 1 - Make a mixture of 10 parts water to 1 part bleach. Wipe on the mixture until the stain is gone. HOWEVER, you want to KNOW that the mixture WILL bleach the wood. BUT, if it doesn't go too deep, then you can sand-out the spot and try to refinish it. Since it's covered over with carpet now, simply re-cover it with a NEW carpet. ONLY treat the affected area(s) because if you manage to 'damage' enough surrounding boards, Option 2 will not be a possibility.
Option 2 - IF there are other boards in the room or even the closet that you can have the Pro use to replace the damaged ones, consider this. DO talk to him about it and what it will entail and what it will look like BOTH in the 'main room' and in the closet.
Option 3 - IF the floor is able to be refinshed, there's no guarantee that the stain will sand out. IF your stain is mainly on the surface (the 'finished' poly surface), then refinishing is an option ASSUMING there's enough wood left to sand.
Now, if you're only option is to replace the entire floor, then yes, I'd rip it out. YOU can save some $$$ by doing this yourself. Get the pro to FIRST estimate the entire job. THEN, ask him how much would you save if you removed the existing floor and trim and all. If it's worth the $$$, consider doing it. And DON'T forget to ask him for some 'tips' on what to do to remove the old floor. And yes, IF you just layed a new floor over the existing one, you'll have a 'room transition problem' due to the height differential. That's why you'd want to remove the existing floor. Doorways and closets too would have a 'problem'.