Archon manning the quad gun

Hows this, An Archon fires the quad gun with his BS of 7, the quad is twin linked so re-rolls misses but his BS of 7 lets him re-roll 1's, if the twin linked re-rolls score a 1 does the Archon's BS 7 get you to re-roll the missed re-rolled from the twin link? or am I just thinking this far too much?

you can never reroll a dice more than once.

You only ever get to re-roll once.

BRB p.5 wrote:

...no single dice can be re-rolled more than once, regardless of the source of the re-roll.

Can't reroll a reroll