Fox's shine does not knock Falcon down. In the air, it just pushes him away - therefore it is "untechable".
However, shine would knock down an opponent Fox/Falco at any percent. Having set knockback means the percent isn't a determining factor of the move's effect when you connect, and varying percentages do not alter the results of successful hit. Characters that fall down from the shine can tech from 0 all the way up to 999%. The "green flash" only appears when a character is knocked against a solid surface. Because Falcon doesn't fall down from the shine, if you got hit into a wall you'd slide along it, rather than bump or crash into it for the tech.
If you get shined and don't touch a wall, no green flash, and no tech. If you d.i. towards the stage when you are getting shine spiked, it may have a positive effect and allow you to tech - but it isn't 100% foolproof. Think of it as an ace up your sleeve if you simply aren't close enough to the sides of a stage.
Characters that don't fall down from the shine:
Bowser
Falcon
DK
Ganon
Link
Peach
Sheik/Zelda
Yoshi
Samus
Luigi
Ice Climbers
Mario
Doc
Marth
Ness
Characters that fall down from the shine:
Falco
Fox
Game and Watch
Jiggs
Kirby
Mewtwo
Pikachu
Pichu
Roy
Young Link