Every character but Bowser can always spotdodge or roll out of single-shine grab. Here's the frame data (for Marth, but almost all characters start their spotdodge and roll intangibility at the same time so it's widely applicable):
http://smashboards.com/threads/good-uses-for-nair.405792/#post-19537867
Here's the frame data for a double-shine where the victim buffers an action on the first shine (also on Marth):
Frame|Attacker|Victim (spotdodge)|Victim (forwards roll)|Victim (backwards roll)
1|Hitlag|Hitlag|Hitlag|Hitlag
2|Hitlag|Hitlag|Hitlag|Hitlag
3|Hitlag|Hitlag|Hitlag|Hitlag
4|Hitlag|Hitlag|Hitlag|Hitlag
5|Inactionable frame of shine|Shieldstun|Shieldstun|Shieldstun
6|Inactionable frame of shine|Shieldstun|Shieldstun|Shieldstun
7|Jumpsquat|Shieldstun|Shieldstun|Shieldstun
8|Jumpsquat|Shieldstun|Shieldstun|Shieldstun
9|Jumpsquat|Spotdodge startup|Roll startup|Roll startup
10|(Shine hitbox active)|Spotdodge intangibility|(Roll startup)|(Roll startup)
The entries for frame 10 are in brackets because the characters are actually in hitlag from the shine at that point.
As you can see, if the victim spotdodges then they will avoid the shine and subsequent grab, and if they roll then they will get hit out of the startup frames of their roll. Almost all rolls are intangible on frame 4, so it's a 2 frame window to hit them out of their roll if the shine is not stale, and a 1 frame window if the shine is stale (occupying somewhere around 2 or 3 positions in the stale moves queue) since that reduces the shieldstun by 1 frame.
Since Jigglypuff's forward roll is intangible on frame 3, she can buffer roll out of double-shine grab if the shine is stale (which is likely to be the case most of the time unless the Fox has just spawned or has been lasering heavily). Jigglypuff is the only character that can do this; the intangibility on both rolls starts on frame 4 for every other character except for Bowser, for whom it starts on frame 5.
