That's possible, although it's really too much of a cluster**** to see what actually happens.
Blue falcon does get a second up-b however, which conceivably could have been awarded from having attacked green falcon or from being hit by shine.
My guess is that even if blue falcon had started his up-b, the shine would have knocked both him and green falcon out of it in the middle of the attack.
Although, I'm not sure if you can actually get bounced like green falcon does in the video off the stage from just a shine...I don't believe there's enough force from a shine to do that, like there would be from a smash attack or something, which might argue more for the case of the up-b.
I suppose if that were right fox technically may not have even shined green falcon. He could have just been hit off the side of the stage from blue falcon's up-b with it looking more like he got shined due to the animation.