I asked Hollis, my mentor, the other day about how much an audio engineer can change the sound of a song before straying into producer territory. Up until now, most of the tools I've been learning about have been fairly technical in their application - microphones, EQs, compressors, etc. But I looked at the next few chapters and they delve into effects like reverb, delay, and modulation; these are things I know from experience that you can get VERY creative with (you can be creative with the more technical tools as well, but it's less obvious to the untrained ear). It's the job of the engineer to make a recording sound professional/presentable. Any major elements in the song's sonic content are up to the artist or the producer, not the engineer.
He told me that it really depends on the client (on ongoing theme in his teachings-which, in all honesty, I fully agree with having worked in a branch of retail that involves customized creations). Some clients, particularly younger and/or less experienced artists, are open to suggestions about how things should sound or maybe changing the way one part sounds, while others have a clear vision of what they want to hear and how the song(s) should sound; in which case, the engineer just pushes buttons/turns knobs for that session. The client I've been sitting on sessions with recently is a good example.
Even though I'm changing fields/positions, my new career may have more in common with how I currently pay the bills than I thought (not that that's a bad thing)...