In feudal Tibet, parents of “tulkus” were indeed often “above average”, in the sense of economic and political power. And the fact that “tulkus” were most often born in wealthy and powerful families used tho enhance even more such families' wealth and power, thus contributing to aggravate and perpetuate Tibet's extreme social iniquity, to the point that at the time of Tibet's peaceful liberation some 95% of the population were serfs of slaves of the remaining 5%. Since tulkus are supposed to be high bodhisattvas and only beneficial to sentient beings, the conclusion follows that many so-called “tulkus” who served to drive such iniquities were just fake tulkus.
For instance, one such “tulku”, born in a so-called “noble” family where just everyone was a “tulku”, and thus supposedly himself a bodhisattva, after having taken and failed to repay a loan to finance some unspecified youthful eccentricity, proudly tells in his self-biography how the head of his creditor was served by his “protector” in a tray, just because such creditor dared to ask his money back! Just incidentally such “tulku” used to be a most active anti-Shugden hater, the foremost one demanding the evil dalie to choose between Nyigmapas or Shugdenpas and distributing anti-Shugden chakras or amulets.
Bottom line, so-called “tulkus” and their parents may be no better than just the average mafioso together with their mafia crime families.