Cat, try going outside in the evening after dark with a flashlight. I'll bet you catch the culprit in the act.
Btw, my money's on slugs or snails, too. A rabbit or deer would have eaten the whole flower. In my daughter's garden in Salt Lake City, the irrigation would come on early in the morning before dawn. I'd go out as soon as it was light enough to see, and pick off literally handfuls of snails from the iris, daylilies and a lot of other plants.
Also, you can't get snails or slugs with salt unless you sprinkle it right on them. It's not good for the soil, and dissolves easily so you would never put enough out that they will have to crawl over it. A good organic slug bait - there are several rated for use in vegetable gardens - will work much better for you.
