[Herr-Flick]

I believe in the old rules you repaired in the Movement phase and it said the same thing. Which is probably where the idea it can be repaired then fire in the same turn comes from.

I seem to remember having my Tech Priest hang out in b2b with my Demolisher for just such occasions with my old Guard army "Da Bloodaxe Blitzkreeg".

The orks's mek's tools allow you to repair a weapon at the start of a shooting phase and to shoot it in the same turn (ork dex pg. 34).
So maybe thats where it comes from