Full Idea
It is because we refer (rigidly) to Nixon, and stipulate that we are speaking of what might have happened to him (under certain circumstances), that 'transworld identifications' are unproblematic in such cases.
Gist of Idea
Transworld identification is unproblematic, because we stipulate that we rigidly refer to something
Source
Saul A. Kripke (Naming and Necessity lectures [1970], Lecture 1)
Book Reference
Kripke,Saul: 'Naming and Necessity' [Blackwell 1980], p.49
A Reaction
This responds to those who say you need transworld identification before you can rigidly designate something, which has 'reversed the cart and horse' says Kripke. Nice.