Perhaps the two group theory is just my memory filling in the gaps. As Hybrid says though, all three items were shown in that flashback.

I don't remember it being two groups, but I do remember Callandor being present, along with the items of the Eye of the World.  And the Aes Sedai mentioned getting the help of "Kodam and his fellows" who were "young and barely touched by the Taint."  As for the Callandor/Dragon Reborn connection, there was a powerful ward on Callandor attuned to Lews Therin's soul.

 

Logically we can reason there were two groups involved anyway--the Aes Sedai involved in the creation of the Eye all died, and we know that took place first, and immediately. The Creation of the Stone occured nearly three hundred years later.

 

Its not as impossible as it sounds, we know many male Aes Sedai lasted hundreds of years in the stedding, and that that is the reason the breaking was so long/not complete. There is no reason some of these men did not stay aside specifically so they could be there to assist in the creation of the Stone. As for why the female Aes Sedai, with their knowldge, did not spread it--well, we know MANY Aes Sedai were killed or stilled by Aes Sedai loyal to the Tower in the early days... but, far more likely to my mind, those Aes Sedai that survived the creation of the Stone joined with the Aiel--we know roughly a dozen joined the Aiel at the same time the Stone was finished.

 

They journeyed into the Waste, and died there.