I've given this a bit of thought. As long as Bob Shane is alive, I think we will all agree, the Kingston Trio lives. The current arrangement is good, but in my mind, basically a tribute band. Allow me to apologize to George Grove, who has certainly put in legitimate time as a member of "Bob's Trio". Without Nick Reynolds, and Bob Shane, then either George, John Stewart, or Dave Guard, I can't recognize an original Kingston Trio. Mind you, the current group's "Zombie Jamboree" is as good as anything sung in 1957!
Ownership of the "Kingston Trio" name, brand, title, will have to be decided, as would assignment of royalties.
A skilled group such as today's members can continue to sing authentic arrangements of K3 songs. On PBS, in concerts, they render a great performance of the Trio's original lyrics and harmonies. Can they be the legitimate Kingston Trio? Yes - if you wish really hard. They don't sound the same to my ear.
George Harrison once stated, "The Beatles can never get back together without John Lennon". I see the same mirrored statement for The Kingston Trio.
If my response injures any one of the current Trio line-up, I ask your forgiveness. You continue to do a service by performing the legacy.