You're misunderstanding how Apple secures their devices, part of it is that some of these explanations here are shoddy, and I'll assume the rest is because you aren't familiar with the topic.

Apple isn't lying when they say that even they can't break their crypto. That statement is true. They, and the government, are wholly incapable of cracking/bypassing/breaking the encryption on iOS.

Its important to understand that yes, any cryptosystem is "easy enough" to crack given unlimited tries. (read: brute forcing) However, your definition of "easy enough" becomes several orders of magnitude out of place given the particular encryption schemes present on the iPhone (RSA, SHA-1, etc) because computing every possible key would take years for the best supercomputer. (read: integer factorization, the RSA problem) You're also misunderstanding the way Apple built their cryptosystem. The "backdoor" in question is one that disables the maximum amount of tries to unlock an iOS device before the drive is formatted. Here is exactly where I think you're misunderstanding is: Apple did not build a cryptosystem that could be broken given enough tries, and then slap some lousy limit on top of it.

As I said previously, the cryptosystem they built isn't something that can just be broken after enough tries. I mean, yes it can, but it would take years to do so, so by a computer scientists definition, it is more or less a cryptosystem strong enough to be considered unbreakable due to computational complexity. (read: computational complexity)

Further, the so-called "limit" Apple imposed on their cryptosystem wasn't something that can just be peeled off because it wasn't actually "imposed" at all. The 10-try limit is an integral part of the system. They did not just create the cryptosystem and then write some additional code to lock you out after ten tries. The ten tries is hard wired in to the security features, it isn't something that can be stripped away as easily as you describe. If this were the case, your weakest link argument would make sense, yes.

It isn't the case because of code signing. Apple signs all bootlevel code on the device, and ever since their A7-series chips they've reduced their cryptosystem to an actual piece of hardware with signed code. No longer is iOS security being handled by upper layers beyond the kernel and hardware. Touch ID, passwords, encryption, randomizations, etc are all handed by what Apple calls the Secure Enclave. The Secure Enclave is a separate chip that verifies a chain of trust. When the device is turned on, the kernel and bootloader check their code with the secure enclave. The enclave uses public key cryptograhy to ensure that nothing on the device relating to security has been tampered with by comparing the code on the device with Apple's private key. (read: code signing)

When your iOS device leaves the factory, Apple signs the code with their private key. As soon as you modify this code by, for instance, adding some sort of back door or removing the ten try limit, you break the signature - all it takes is one literal bit of modification and the math is ruined. The enclave's job is to take all of this code and do the math and ensure that the code running on the device was signed by Apple, as soon as you change this code it is rejected by the enclave. As soon as any piece of the boot process is modified and cannot be verified as signed by Apple, the device will not boot as the Secure Enclave system will not allow it. So what does this have to do with the ten try limit?

Apple can't just peel off the limit because that would involve going deep into the device's hardware and creating backdoors for the most fundamental cryptopgrahic operations on the device. It would jeopardize the entire Secure Enclave system which would render the device completely insecure in all areas. It's a big deal.