So these are not AC flights, but rather Jazz. Just as Great Lakes aviation doesn't fall under UA, or even UAX, they do codeshare with UA (as well as F9 and others, if I recall.)

I don't know how Jazz fits into the star alliance, but some of the European * carriers regional partners are not members of the *A either. I am looking at a picture of a jazz aircraft and I don't see the *A logo on it, nor are they listed on the *A website. The *A website (www.staralliance.com) does mention Jazz when giving info about AC, but again, I am not sure if all routes or flights, or what they consider dual codeshare (code sharing on AC and by the transitive, on UA) in order to get a UA flight number (which shouldn't be required) or what their specific relationship with the * is.

Maybe under www.flyjazz.ca you can find some answers to the questions I pose