I think it used to be that Seigan did nothing unless you had Third Eye up. (except Fast Cast-)
Then with Abyssea and the introduction of AF3+2 we got the hat to allow you to counter with Seigan, even when TE is down.
Then, we got a SAM update:
Hasso - you can now Zanshin. (on melee swings)
Seigan - you can now counter. (without TE)
...so when wiki says "gives a chance to counter w/o TE being up" really confused me.
Basically wiki's refering to the time before the Seigan update where you could only counter with TE up.