Well, no, not strictly. First, Einstein is not "the science god" in the sense of infallibility; Einstein made a bunch of mistakes. His proofs of E = mc², for example, were pretty uniformly inadequate. Others have since proven the statement much more rigorously. His journals show that he made several huge time-wasting blunders at first when he was working on general relativity. And so on.
Einstein's statement is a reaction to the Copenhagen interpretation of measurement. The uncertainty principle is very different.
Look at it this way: we can get quantum mechanics to be deterministic if we commit ourselves to the objective reality of the wavefunction ψ. Then ψ evolves deterministically according to the Schrödinger equation, which guarantees the Heisenberg uncertainty principle directly. (The Heisenberg idea: as you try to fix the position of a particle precisely, you require it to have a small size, and therefore a small wavelength. Since de Broglie observed p = h / λ, where p is the momentum, λ is the wavelength, and h is Planck's constant, compressing λ leads to a corresponding broadening of p.)
What Einstein was objecting to was very different: he says, ψ isn't enough. Why not? Well, because: it is possible for my television to occupy two different places in my house: living room and bedroom. In the Dirac language of quantum mechanics, we could say that:
| TV > = a | bedroom > + b | living room >.
With the condition that |a|² + |b|² = 1.
Now, there is an aspect of the above quantum mechanics which Einstein didn't understand then, but which we now understand much better, called /decoherence theory/, which says that, given the amount of light and air molecules getting caught up with the TV, this quantum superposition must become a classical superposition: |a|² in the bedroom, |b|² in the living room, with no more quantum interference terms. Quantum effects disappear.
However, here is the problem, called the measurement problem. We don't see a television which is |a|² in the bedroom and |b|² in the living room. Not unless we drop it off of the roof, scoop it up, and put it in two piles in those respective rooms! No, the television is either in one room or the other.
This also happens with light. We get these beautiful wave interference effects with light, but ultimately, our photomultiplier tubes register distinct clicks when a photon hits them. The wavefunction ψ which describes the light is distributed over many distinct photomultiplier tubes: but instead of all of them firing a little, one of them fires a lot.
So the light has to "make up its mind" at some point, even though our best description has the light's wavefunction distributed over all of its options. The Copenhagen interpretation, which Einstein was objecting to with this quote, says that it works like this: the light particle just chooses randomly from its options, weighed by |ψ(o)|² for each option o. Einstein was saying in effect, "no, there has to be something which *causes the light* to choose *this particular option*."