Your friend is absolutely wrong. It is not "designed that way", it is a defect and should be repaired.
"Brinelling" is a misnomer but it's used to describe the pockmarking of the headset races (usually the lower race) due to impact, lube breakdown and wear. The pockmarks align with the bearing balls and cause what is called "index steering" or the self-centering you mentioned. It interferers with the proper steering of the bike and in serious cases can be dangerous.
A quick and temporary fix is to replace caged balls with loose balls. That requires one or two more balls per race and the pockmarks no longer line up with the balls. The proper fix is to replace the headset with a new one followed by proper adjustment and lubrication to keep it from happening again. .