I guess the point atyy makes is valid if you were exposed to the Copenhagen doctrine long enough, in the following sense. For definiteness let's discuss the Aspect experiment in ultrasimplified form, i.e., not considering wave packets for the photon states, which in principle is, what one must do for a fully correct description, also with respect to our discussion here, but I have to formulate this carefully, before I can write it down here. So let's do the handwaving arguments with considering polarization states only and just add the space-time aspects of the measurement procedure "by hand".
You start with a two-photon Fock state with entangled polarization states (usually prepared, using parametric downconversion and appropriate phase shifters for one of the photons), represented by the following ket:
$$|\Psi \rangle=\frac{1}{\sqrt{2}} (|HV \rangle-|VH \rangle).$$
The single photons are in mixed states (using the standard reduction formalism, by taking the trace over B's photon to get A's photon's state and vice versa) is for both
$$\hat{\rho}_A= \hat{\rho}_B=\frac{1}{2} (|H \rangle \langle H|+|V \rangle \langle V|,$$
i.e., the polarizations of both single photons is maximally uncertain (maximum von Neumann entropy).
Now Alice and Bob have detect at far-distant places at the polarization of one of the photons respectively. Due to the geometrical setup you can by a precise enough measurement of the time of the photon detection make sure that A and B always look at two photons belonging to the entangled pair. Suppose now that Alice is much closer to the photon-pair source than Bob, so that she detects her photon way before Bob.
I'd like to also discuss the most simple case, where Alice uses a polarization filter letting horizontally polarized photons through and Bob one letting vertically polarized photons through. I think there's no debate about the outcome of the measurement when A and B compare their measurement protocols (modulo detector inefficiencies which can be made arbitrarily small nowadays, so that we can neglect it for our idealized description): If A detects a then necessarily H-polarized photon, Bob also detects his then necessarily V-polarized photon, and if A doesn't detect her photon, also B doesn't detect his.
Now let's discuss the experiment from the point of view of a Copenhagen-collapse interpreter (which I heavily disagree with) and from the point of view of a minimal interpreter (I heavily agree with)
Copenhagen-collapse interpreter's point of view
Suppose, A detects her photon (which happens with 50% probability). Since it's then for sure H-polarized according to the Copenhagen collapse mechanism, after this measurement the entire state collapses instantaneously to the state described by
$$|\Psi' \rangle=|HV \rangle \; \Rightarrow \; \hat{\rho}_B'=|V \rangle \langle V|.$$
I've already renormalized the ket to be of norm 1 again. So taken the subensemble, where A detects her photon, then B for sure also detects his photon, because it's vertically polarized.
Criticism against this view
This point of view violates relativistic causality and contradicts the very foundations of QED, which is (I think also undoubtedly) the correct model to describe this experiments, because if there were a collapse like this, the detection of A's photon must instantaneously change the state of B's photon from ##\hat{\rho}_B## to ##\hat{\rho}_B'##, i.e., from "maximally uncertain" to "determined".
Now, by construction, this contradicts QED by construction: The interaction of A's photon with her polarization foil and photon detector is local from the point of view of QED, because QED is constructed as a local relativistic QFT, and there can be no FTL signal propagation (note that such signals are described by the retarded propagator not the Feynman propagator as in classical electrodynamics!).
So, as atyy said, if you want to invoke the collapse argument, you must not misinterpret it as a real physical process, and the 100% correlation between the outcome of A's and B's polarization measurement cannot be satisfactorily explained by the collapse. It's an ad-hoc assumption to apparently simplify the prediction of the outcome of the measurement.
Minimal interpreter's point of view
There's no need for the collapse to explain the result of the experiment in terms of QED. You just evaluate the transition probabilities according to the corresponding S-matrix elements. In this case, you simply have to take "wave-packet states", leading to a detection probabilities as a function of the times and locations of A's and B's detection event ("click of the photon detectors"). The result is of course the same: 100% correlation between the single-photon polarizations, but nowhere did I invoke a collapse argument.
As I said, I should work out this in mathematical form using standard QED (quantum optics to be more precise, because one has to use the standard effective theory to describe the optical instruments involved, i.e. in this case, polarizers).