When you install Scala using Homebrew you are told
To use with IntelliJ, set the Scala home to:
name := "HelloScala"
version := "1.0"
You need to set scalaVersion in your sbt file or else sbt will use the scala version it was built against.
scalaVersion := "2.11.0"
This will make sbt automagically download the scala 2.11 jars into your ivy cache. Both SBT and IDEA will then use that to compile and run your scala code.
So you wouldn't actually need to install it with homebrew at all unless you want to be able to run the scala repl in a console/manually run scalac etc.
It's only when you do not use the SBT integration you need to point out your scala installation in IDEA.