This information is incorrect. Yesterday, I was able to emulate (thought this was the proper word considering Thaum's past) Legacy's strategy with two different linkshells. In both cases, all five of the BLMs had an intelligence of sub 360. In one group, only three of the BLMs actually had double melds, and one was only using double melds of Tier III int materia (+24 on head and brand, +12 on legs) while the other (myself) had only the equivalent of a double IV int hat, double IV int pants, and a double IV acc. scepter.
The important thing in this fight is making sure you don't get resisted, the rotation of your BLM spells, the timing of your abilities, the timing of BV while using convert to maximize MP gain, and knowing when to both rest MP and when to burn through your MP to take it down.
To be fair, though, both of the kills only occurred after Garuda had teleported and was readying AF. So it was VERY close. But the notion or concept that 370-380 Int is a requirement is not true. Additionally, both groups could probably continue to optimize the fight through better spell/ability rotations to increase the kill speed so that it could be done before the teleport into astral occurs.
P.S. Thank you to both Darth Taru and Lux Aeterna for taking the time to talk to me about how to stagger nukes through the first to second teleports to extend the time before Astral Flow occurs. The strategy is incredibly clever, even if it will probably only last the duration of Golden Week =P.