Hopefully this wont sound insulting...
See that large box near the top saying "Shared Cooldowns"... :) Does it list the Insignia? Yes. Therefore they share the same CD.

Also, it doesn't stop spells from landing on you. It merely removes all slow/root effects on you (Fear, Polymorph, frostnova, poison, hamstring, wingclip, kidney/cheap shot). I'm fairly sure some moves (possibly gouge for instance) will not be affected as you cannot activate the trinket while under its effects.
THIS DOESNT PREVENT THE ENEMY REAPPLYING THE EFFECT!
If you trinket to remove hamstring, they can immediately reapply it leaving you with a wasted trinket on CD.

Its also fairly cheap. ~16k of honor, of standard effort in a BG (1k an hour) thats 16hours. Split this into a few days of 2-3hours a day (+the PvP daily of 400 honor) and you can get this in a week like most other gear.
For hardcore/good PvPers (>=1.5k an hour) its even less :D