Some repairs (such as iMacs) do require a substantial amount of care. Even after 8.5 years of Mac repairs I still found myself running into issues - from "fat fingering" connectors, to defective Logic boards that still pass all hardware diagnostics sent to us - some of this stuff is not for the faint of heart. Imagine using a plastic "pizza cutter" to cut off the VHB tape that holds the incredibly fragile $800 display of an iMac, and then remembering to connect the display back up before you put new tape on during reassembly.
My guess is Apple fought the NY bill because they know how these machines are designed. There's a reason they charge a flat rate of $39 for Labor, but then only when a hardware repair is actually completed.
On the other hand, the charge to backup your data is $99 for a drag/drop or a time machine backup - something you should do yourself. :-)