Let's consider the incentives in each case and how they enable you to distribute your trust. Apple is a for-profit, publicly traded corporation. Their purpose is to make money, and they will likely do whatever they can to achieve that. More importantly, only they can see their code, not you and not other users. All you can possibly have is their word, and they will say whatever it takes to sell you their product. If they lie or exaggerate, there's no way you or anyone else could know.
On the other hand, open source projects come in all shapes and sizes. Generally, they have a strong community of both developers and users around them. If you don't feel like looking at the code, you don't even have to trust the project itself. You can look to the community and its abundance of users, at least a few of which have audited the code and share your use case. And these users aren't just neutral third parties. Nay, they're better than that. They, too, value their own privacy, and are therefore motivated to protect it.
This is silly. Apple publishes their privacy policy. If they were found to be violating it, they would lose business and be liable for expensive lawsuits. And security researchers are extremely good at finding these things. So yes, Apple has a very powerful incentive to tell the truth.
As for the theory of "open source community," see the MyBTGWallet scam. This open source project, recommended by the Bitcoin Gold team, stole $5 million via a single line of code. Being open source isn't much protection really.
He's telling you about the fact that there's conflict of interest between you and crapple and you tell him an anecdote where some scum of this earth stole money and open source software was involved. Does this really sound like a compelling argument?
It does however increase the chance that it will be bad, because the average snake that produces closed source software is likely to be motivated by greed, so it has the incentive to milk you as hard as it can without turning you away from products (using lies of course, you can't check anything after all, it's closed shit).
But seeing sibling explanation being downvoted into oblivion makes me think no one is interested in discussing this anyway so why waste breath.
On the other hand, open source projects come in all shapes and sizes. Generally, they have a strong community of both developers and users around them. If you don't feel like looking at the code, you don't even have to trust the project itself. You can look to the community and its abundance of users, at least a few of which have audited the code and share your use case. And these users aren't just neutral third parties. Nay, they're better than that. They, too, value their own privacy, and are therefore motivated to protect it.