The following is the analysis a non-professional, not-even-licensed-to-practice-anywhere law student only.
Even though Spielberg may be a bona find purchaser (BFP), meaning that he bought the painting from somebody he subjectively believed had the ability to transfer title to him and this assumption was objectively reasonable, he does NOT have better title than the original owner of the painting. A purchaser of goods can only acquire the same title as was held by the seller. Here, the seller had a VOID title, because the painting had been stolen. Spielberg therefore didn’t purchase good title, and he’s going to lose out to (at least) the original owner even if he’s a BFP.
There are a few ways that a BFP can get title even superior to that of the original owner, but they aren’t applicable here. That’s probably what DxZero was thinking of when he said Spielberg wouldn’t have to give the painting back. He’s right, though, that if Spielberg is a BFP (which he almost certainly is), he won’t be subject to any civil or criminal liability.
Another way Spielberg might have title to the painting is through adverse possession. To claim title through adverse possession, you must act like the owner/assert control over the property in question in such a way as to provide fair notice to the true owner that you’re staking a claim against his or her property. If the statute of limitations (the amount of time the true owner is allowed to bring suit) runs, congratulations, you get to keep the property! It’s pretty hard to use a painting in such a way that it should give notice to the true owner that you have it, unless you’re displaying it in a museum or something. As a concession to this, the law in most states says that the statute of limitations doesn’t start running against the true owner as long as he is “reasonably diligent” in seeking his property.
Now, I have no idea what the statute of limitations for this type of action is in California (or whatever the forum state). I also don’t know whether the true owner was “reasonably diligent” in seeking the painting, thus preventing the statute from starting to run. It does seem that the bar for “reasonable diligence” might be pretty low, though. See, e.g., O’Keeffe v. Snyder. Since the painting was presumably reported stolen at the time of the theft, I’m guessing the statute of limitations never started to run, and therfore Spielberg couldn’t claim adverse possession.
All of this is a long way of saying that even if Spielberg wanted to keep the painting, he probably doesn’t have the right to do so. If he wants to get his money back, he probably has a cause of action against the gallery or its successors.