Earlier quoted context omitted.
All public encryption algorithms have backdoors in their implementation and sometimes (as with Elliptic Curve standards from NIST adopted in the browser) in their spec. You might get lucky if you have a cryptographer design you a custom algorithm but that's mostly security thru obscurity and if a state actor really wanted to defeat it they may just kidnap the cryptographer at gun point and have them reveal how to. Cr…
Although you're right that anything but OTPs give you guarantees and that cryptography is still a black art (with lots of unrealistic conditional proofs), good cryptography can be completely open and will be no less secure if it is published, so there is really no need to kidnap the cryptographer. There is also good reason to assume that if e.g. you make your own Feistel cipher out of existing cryptographic primitive…
The key is "your own"
By "public" I don't mean that their spec is "published" but that their implementation is open source and has various 3rd party contributions and dependencies, as is the case with most OSS.
So if you build your own, and it's good against the NSA, they'd come after you if they have to, unless it costs them less to crack it.
I agree ultimately with your assessment that side channel attacks make this whole discussion moot. But my original point was and still is: nothing is secure against a determined and well resourced adversary. So people out there shouldn't get the wrong idea that cryptography is an invisibility cloak or some such