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Non-Locality – (just ) one more question?

I have read comments that Bell’s theory proves quantum mechanics is non-local, and also comments that it does not. I have read a comment by a very eminent person who stated what it means is that a measurement of a particle at one location "influences the state of the other particle". So my question is this: Two particles in the singlet state (as always) go their separate ways. At time one each passes through a SG apparatus with orientation in direction $z$. At time two particle 1 passes through a second SG apparatus but with orientation direction $x$; nothing happens to particle two. At time three the spin of both particles is measured in direction $z$. What will be the outcome of the spin measurements?

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Wouldn't the first measurement at time one destroy the entanglement? I would think that for particle two, whatever result you got from the SG apparatus at time 3 would be the same as the result for particle two at time 1....

Here is a rather helpful and insightful blog post by Chad Orzel that may clear up some points about entanglement: Entanglement is not that magic.

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Bell's theorem is a mathematical result. It states that if the outcomes of measurements are described by stochastic variables then those variables have to be non-local to reproduce the correlations predicted by quantum mechanics. But quantum mechanics isn't a theory about classical stochastic variables. Rather, the physical quantities that describe the evolution of a quantum system are Hermitian operators that evolve entirely locally:

http://xxx.lanl.gov/abs/quant-ph/9906007

http://arxiv.org/abs/1109.6223

These operators describe physical reality as being a more complex structure than the universe as described by classical physics that, in some approximations, resembles multiple non-interacting versions of the world as described by classical physics.

For each measurement there will be two versions of the measuring apparatus after the measurement. One of the versions of the measuring apparatus will record spin up, the other will record spin down. When a joint measurement is done on records of each result they then become correlated.

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