Is conditional branching a requirement of Turing-completeness?

Question

I\'ve been searching the web and I\'m finding somewhat contradictory answers. Some sources assert that a language/machine/what-have-you is Turing complete if and only if it has

Answer 1

The Z3 was only Turing complete from an abstract point of view. You can have an arbitrarily long program tape and just have it compute both sides of every conditional branch. In other words, for each branch, it would compute both answers and tell you which one to ignore. Obviously this creates exponentially larger programs for every conditional branch you would have, so you could never use this machine in a Turing-complete manner.