This is not true. Especially in the case of a sealed integrated headset, you just pop out the old bearings and pop in a new set.

In an integrated headset with lose or caged bearing (which seems unlikely): if you let the headset go to hell (meaning the bearing are left dry, or with grit inside, or adjusted incorrectly more a period of time, start to pit the cups, thus destroying them) you may well be looking at a new frame. Most "good quality" integrated headsets will be sealed for this reason.