My understanding is the door has to first move DOWN to get the top lock pins out, compressing the springs, and then it's UP and out. But I could be wrong.
The bottom bracket screws found loose on the United planes, I think are the second mech failure here. Once those screws fall out...
Here’s the latest video from the 737 expert that provides a thorough description of the plug attachment system.
https://youtu.be/5FcyvFfHsjQ?si=0rryavmB2_SfNs1RThe brackets are on the plug, and the pins are on the aircraft door frame.
The springs, incredibly, act to push the door up and into the released position. The installers have to push the door down against the springs in order to get the locking bolts in.
I speculate that since there doesn’t seem to be a handle/leverage point on the inside of the plug, when it came time to put the 4 locking bolts in, there was no ladder outside for someone to help push down the plug against the springs so the bolts could be inserted.
The installer doddled off to report it, the interior guys replaced the wall coverings, and the bolts never got installed.
The design, while clever, was a bit too clever in the use of the springs to aid plug removal when necessary.
Further, if the pins and bracket arrangement had been reversed, with the pins on the plug and the brackets on the door, then indeed the springs would have worked to push the pins into the brackets. Perhaps this was the original design thinking, but something happened to cause the pin/bracket swap during manufacturing changes.
Apparently, other doors in the aircraft normally have pins on the door and brackets on the door frame. So perhaps a change that caused unintended consequences. Below is the relevant image from the video that shows the arrangement of the plug "guide track" (what I've been calling the "bracket"), and the door frame pins.