I'm still not convinced this techinique couldn't be done in Brawl.
In Brawl, stopping can cancel a dash. Stopping is done by letting go of the analogue stick, just like run stop, while dashing. Like OP described, the stopping animation in Brawl can be interrupted.
Tilts and smashes can be buffered in Brawl. Buffering is a tool that allows inputs to be executed as early as possible. Hence the frame where a buffered action starts is called the IASA frame (interruptible as soon as frame). So the frame before the IASA is effectively the end of the previous action; the last frame where you can't do tilts or smashes. This end, for stopping, happens before the stopping animation seemingly ends like Lucario's fsmash or Marth's dtilt. Point being, stopping could appear to be cancelable by tilts and smashes if done after that end. Although you can cancel a stop with some moves in Brawl.
The speed of run stop in the demo, and so the attributes described by OP, could just mean run stop effectively ends sooner than stopping does in those Brawl videos I showed. I know this is likely the case with Bowser. Although my reasoning is fairly long.
A while back, I thought perhaps other characters followed Bowser's trend and eventually I got to briefly test four characters at an event in London. Bowser seemed as fast as my research suggested; Bowser's run stop ended notably faster than Brawl. The run stop of Pit and Luigi seemed about the same. WFT's run stop seemed long. Usually I play at 1/4 speed and work up to full speed to get a feel for the buffer windows for stopping in Brawl. Even though I couldn't do that for demo, I'm pretty certain I did buffer for all four of those characters.
Depending on how this post is received. I could talk about other features of stopping in Brawl that perhaps apply to run stop in the demo and the final build which admittedly is a big reason why I wrote this.