Tight assembly is not the problem. Any mechanic who has seen a lot of the older type cone and cup headsets is familiar with "brinneling," which is why you see the fixes above that have been used for years. One can actually often see the dents in the lower headset cups. One generally can partially fix the problem just with work on the lower bearing. Of course the correct solution is a new headset.

Also, rather than addding one bearing to the amount in the cage as noted in an earlier post the proper count for a headset is to full up the entire cup until the last bearing crowds the others and then remove that one.