I don't know who the hell Dave Kellett is, but he said that.
Apparently, this is his work.
Lisa Marie Presley recently released an album. I've heard one track, and I liked it. And what I've heard about the album is positive. Jakob Dylan was and is in a band called the Wallflowers. Back in the 90s, they released Bringing Down the Horse which contained "One Headlight" and "6th Avenue Heartache", and they contributed a pretty bitchin' cover of a David Bowie tune to the Godzilla soundtrack. Ziggy and Damien Marley are fairly accomplished musicians in their own right; Damian has three Grammys under his belt, and contributed to the "supergroup" SuperHeavy last year, and Ziggy has released around 20 albums. Julian Lennon has released six albums to date, and has had at least one major hit with "Too Late for Goodbyes".
These are extreme examples, to be sure. The success of their parents can't help but eclipse the success of these children, unless they go into another field (one of Bob's sons, Rohan, played pro football), or change the game completely (thus far I can think of no examples). The phenomenon seems largely limited to music, though. I can't think of any famous writers whose kid(s) tried their hand and succeeded less. Actors often succeed as much or more than their parents (Kate Hudson's done all right. And I'm sure that Lon Chaney Sr. was quite proud of Lon Jr.) Politics is also fond of heredity, even in democracy (I still can't believe the success of the Bushes.) And athletics actually seems to foster (usually) father-son relationships. Particularly baseball (see Griffeys and Ripkens).
A notable (possible) exception to this rule is Norah Jones. Ravi Shankar is a legend, and it looks like Norah's on track to be as well.
I'm not planning on weeping for the offspring of musical legends. I suspect their childhoods are hard, certainly harder than mine was, for several reasons: familial instability, travel, drug abuse, and the media spotlight. But there are compensations. Being shockingly wealthy, for instance. Or, if you choose to pursue music, you already know producers and musicians and writers and journalists and executives and other people who are likely willing to give you a chance.
But it's interesting to note the parallels between the children of legends and their careers and the careers of legends after the legend is over. Damian Marley is a successful musician, by any measure. He has had commercial and critical success, and he has the respect of other legendary musicians. But he will never be his father. Wings is a successful band by any measure. They have had critical and commercial success (as well as an Academy Award nomination). But Wings will never be the Beatles.
Having famous parents is clearly a double-edged sword. Breaking into the arts is easier, but the comparisons will not favour you.
Politics is the only safe place to follow in you parents' footsteps. But even that's not a sure thing. Look at the Skywalkers.