Here's the quote with a bit more context:
"We're going to double down on
secrecy on products," Cook said, but on
other things, "we will be the most
transparent company in the world," -
like social good and supplier practices.
Double down is originally a blackjack term to play for double or nothing.
It is used more generally to mean make a calculated gamble to double your commitment, to concentrate or focus on something.
But it seems like use is changing, and it's simply means you will try twice as hard (as there's always some inherent risk in everything).
Cook is simply saying Apple are going to be more serious and committed about product secrecy.
The linked question asks about:
is notorious for doubling-down on
perceived missteps, typically blaming a biased media for not
telling the whole story.
This is similar; Sarah Palin concentrates and pays extra attention when people claim she makes mistakes, usually trying to deflect blame to the media.