not totally true on either account. Sometimes people can break fingers and not even know it, until they stop the activity they are performing. Once you come down from the "high" of a competition, you can notice the pain. The whole endorphin thing, trust me on this one, I dont want to get too technical. Also, it depends on the joint and the type of break before you truly know how long someone can be out. It could be displaced, although not to the naked eye and it may require reduction. Also, if it lightning rodded vs a simple transverse break, it could cause him to be out for longer. Another thing to consider is that many hand breaks may not even be evident on XRays for a week or so, so sometimes you call it a break before you actually see it on the XRay.
As far as swelling, sprains are associated with a ton of swelling initially because there is usually twisting and breaking of blood vessels due to the sheering force and the swelling is due to extravasating fluid from your busted vessels. As far as breaks, they are usually from blunt trauma and not a sheering force, so your body responds to the injury with inflammation by trying to heal it and hence you will swell over time as your body responds to the injury. This is a horribly simplistic view of it, but with finger injuries/breaks, you could be out 3 months or a week, so wait for the report. There are way too many scenarios to even consider....