Shutter Speed controls ambient light and Aperture controls flash.
It disturbs me when people say that, especially to the inexperienced. Whilst it has some truth in that shutter speed does not affect flash power when below max sync, it is misleading in that aperture does affect ambient and flash (if the flash is in M and you don't change the power level).
Shutter speed - ambient control (limited by sync speed. Which is why strobists crave high true sync speeds)
Aperture - affects ambient and flash exposure. (NDs can allow you to get the smaller f-numbers.)
ISO - affects ambient and flash exposure. (For speedlites, I start at iso 400 to get faster recycles with less power when ambient light is low.)
Then there is high speed sync, inverse square law, big mods vs small mods, etc... but the fundamentals stay the same.