Tahoe-LAFS providers like Least Authority [1] and Matador Cloud [2] pride themselves on not being able to access your data.
With Tahoe LAFS, you're either downloading the pre-built binary or compiling from source. Either way, you're trusting the person who signed the binary/source or the person who hosts them.
This is similar to when Apple says they can't read your messages. Sure, they may not able to decrypt the data on their server, but they're in total control of the client software. They can get access to your messages.
I do think it's in Tahoe/Apple/etc's interest to NOT be able to see their data. For one, they said they can't and reputations are important. It may also be beneficial when dealing with law enforcement requests. So trusting them isn't totally unwarranted, but there's a lot there that isn't mathematics.
(You're never going to get to 100% math, but there are ways to get further. For example, someone might eventually write a Tahoe LAFS client that comes with a machine-checkable proof that it doesn't leak plaintext. You now need to trust the proof checker, but it's progress.)
For example, people should know that blanket statements like "Apple cannot read your messages" are false. And your client/server protocol can be state of the art, but you still rely on the much-maligned HTTPS certificate infrastructure (among other things) to get the client bits.
I believe you can architect a solution such that it's easy enough to get a third party (or yourself) to verify it is safe and private, even in the face of a hostile backup provider (or more realistically, a backup provider that's met an opportunistic law enforcement agency waving a sternly worded letter).
If enough parties collude, they can still gain access to your data, but at that point I'm pretty sure the backups won't be the weakest link anymore.
I mean, you're still running an OS, and compiling with a compiler, installing and running software from a package distributor, and using a CPU with a management engine, and all those things might have backdoors too.
If this space is interesting to you, spending a few days reading through their Trac is educational and rewarding! Highly recommended.
Trivia: One of the founders of LAFS went on to found Zcash, the (actually) zero knowledge crypto currency.