Question: Assuming space is expanding (and that seems plausible), photons from a galaxy that have been traveling for 12 billion years must have been traveling on a curve to get to us due to the fact that where we see the light today is not where the object is now. And yet there is no distortion in the light from that galaxy. Why?

Answer: 
You and your buddy are standing on some kind of sheet of stretchy material. Someone is slowly stretching the material in all directions at once, which causes you and your buddy to slowly get further and further apart. Your buddy rolls a ball towards you. When you rolled the ball, you and your buddy were 20 feet apart. As the ball rolls, the sheet is, as described, expanding. By the time the ball reaches you, you and your buddy are 25 feet apart.

Analogy key:

* you = telescopes observing distant stars
* buddy = distant star
* ball = photon
* stretchy sheet = space
* person stretching the sheet = dark energy?? TBD.

As you can see in this analogy, no curved paths or distortion are necessary.
Generally it does not travel on a curve. Just the space through which it travels has expanded. There is no need for curved trajectory to explain the expansion of space.