This is absolutely right. If you look at the picture in my sig right now, the top and bottom of the heart was done fair isle and the center was done intarsia. For the top and bottom parts, I didn't strand both colors all the way to the ends of the rows, nor did I have mulitple bobbins. I still call this fair isle, though, because I was stranding the unused color across the back. If someone has a better name for this, please tell me.
It is possible, I think, to make pictures to a certain extent using fair isle. I could have done that heart entirely in fair isle if I had wanted to. To keep from having ridiculously long floats,you would have to weave in the unused color at the back of the work every few stitches, at least every inch or so. It's technically possible, I think, to carry along a color you weren't going to use for many many rows without having floats of more than 4 stitches and without the unused color showing through, though I'm not sure why anyone would want to do that. Fair isle will make any extra warm and thick fabric that intarsia won't because there will be two strands all/most of the time. This also means that it uses WAY more yarn than just doing intarsia would.
I understand the intarsia dislike. Even with just the middle part of that heart, having two brown balls on either side and a multicolored ball in the middle, I was annoyed. Fair isle has its annoyances, too, though.