If it is getting "sikat", then blame the records companies and not the parents of the "rich" musicians.
The better known bands are better known because of marketing plain and simple. It isn't about skill either. If that were the case, then music teachers should be more famous than their students.
When a record company will see $$ signs from a band, they will sign up the latter and milk them dry. It's just business. Nothing illegal.
If there was any direct relation to popularity and rich parents, I think it would be in that the rich kids, like was what previously mentioned, have the time and resources to improve their skills, pay for a demo tape and can book a club for a gig. In the gig, they don't care if they get paid or not. Then they "pay" an A&R guy to watch them.
Buti na lang, this wasn't about why good looking bands without skill are more famous than others.