Well, that rules out 99.9999% of all mobile phones for you, then, with a +/- .0001% margin of error. :-)
I don't "trust" any of these providers. I expect them to fuck me. I just don't get the option to use none of them if I want to participate in modern society.
Open source is not even slightly immune to those sorts of issues.
Which issues? Not being able to trust that the code doesn't do things which are intentionally malicious? It's as close as you can get. Literally all closed source software is less trustworthy.
You're missing my point. To the best of my knowledge, you can't buy a phone that has an entirely open source operating system now; the phone hardware vendors provide closed-source bits preinstalled, and nuking them is problematic at best. More importantly, even if that were not true, you still would not be able to buy an Apple iPhone or iPad with an OS that is pure open source, which makes your concern entirely irrelevant in this context.
This discussion is about what Apple would need to do to satisfy people with privacy concerns when it comes to third-party replacements for Siri on devices that Apple makes. Arguing that you don't trust Apple because parts of the OS are closed source is irrelevant, because you won't ever trust their device in the first place (or any devices, in all likelihood).
Either way, the automatic presumption is that if a consumer does not trust the device maker, that person will buy a device from some other manufacturer. So for the purposes of this discussion, the decision by the consumer to trust Apple is in the past. It was made when they bought the device with a preinstalled OS. Thus we can presume that the consumer in question therefore trusts Apple to a great extent.
What remains, then, is what Apple, as a presumptively trusted party, would have to do to continue to maintain that level of trust in their devices while allowing third parties to inject code that deeply integrates with every app on the system in a highly invasive way.