First of all, have a read over this site:
http://www.ibike.org/encouragement/travel/bagregs.htm
Secondly ... yep, it does sound like you're missing something. You're missing the whole point. Of course we cannot get our regularly-sized bicycles into a box that measures a total of 62" or less ... that's the whole idea behind picking that measurement! Since we cannot do it, airlines can put bicycles into a special category and charge special rates for them.
Keep the box under the weight limit, arrive early, smile and be friendly ... and you'll get away with the normal charge for the bicycle
Go overweight, and you'll be charged overweight rates in addition to the normal charge for the bicycle
Get upset about it all, and you'll be charged oversize (and overweight if they can) rates on top of the normal charge for the bicycle.
It's about that simple ... oh, and be selective about the airline you choose. Again ... read the site I linked to.