They never once mentioned the word Boeing. Every news article about the incident mentions the plane type, but not this skit.
The plane in the green screen backdrop at the terminal isn't even a 737. The side windows on the cockpit of a 737 are lower than the front, on an A320 they're in a straight line like in the skit. I'm pretty sure that's an A320.
Maybe the SNL lawyers were scared of getting sued and vetoed earlier scripts, or maybe they got paid off, or maybe my wife is right and I'm just a skeptic, but that seems suspicious.
On the other hand, the aircraft taking off with a slide deployed is a 737, so maybe they were working mostly with off-the-shelf assets to complete one skit in an entire show of same, and saved the relatively time-consuming animation work for where they had to use it.
Presumably they assumed no one would be paying all that much attention to stuff like an aircraft out a terminal window in the background, which looks nothing much like Boeing or Airbus and would not much surprise me to learn was produced by a diffusion model.