You're conflating very different scopes of "capability" and responsibility.
I'll quote the DoJ's legal brief on how Apple is not "far removed" from this phone owned by a 3rd party:
"... the government is seeking to use capabilities that Apple has purposefully retained in a situation where the former user of the phone is dead ..."
"... iPhones will only run software cryptographically signed by Apple ... Just because Apple has sold the phone to a customer and that customer has created a passcode does not mean that the close software connection ceases to exist; Apple has designed the phone and software updates so that Apple's continued involvement and connection is required."
"More generally, the burden associated with compliance with legal process is measured based on the direct costs of compliance, not on other more general considerations about reputations or the ramifications of compliance".
The DoJ is just re-iterating what everyone knows, which is that Apple can push software updates to a phone.
That does not in any way explain why Apple should be compelled to write new software, that they would not otherwise choose to write, before pushing it as an update.
Apple retained the ability to push updates to improve the performance and security of products, not to make it easier to hack them. There is a difference!
I'll quote the DoJ's legal brief on how Apple is not "far removed" from this phone owned by a 3rd party:
"... the government is seeking to use capabilities that Apple has purposefully retained in a situation where the former user of the phone is dead ..."
"... iPhones will only run software cryptographically signed by Apple ... Just because Apple has sold the phone to a customer and that customer has created a passcode does not mean that the close software connection ceases to exist; Apple has designed the phone and software updates so that Apple's continued involvement and connection is required."
"More generally, the burden associated with compliance with legal process is measured based on the direct costs of compliance, not on other more general considerations about reputations or the ramifications of compliance".