There definitely are "issues" with the AC and LH systems talking with each other.
They are correct that the agent in Phoenix is not an AC employee and it works in your favor that the AC person you spoke with acknowledged it was the fault of the checkin agent in PHX.

I would absolutely write in and ask for compensation, telling them their own staff acknowledged that their contractor agent screwed up. According to their own terms you should be entitled to C$2,400 compensation, so that's what I would ask for.
https://www.aircanada.com/content/da...pdr/ACF520.pdf

I presume if you ticked "Herr" and "Doktor" it is because you are in fact a male doctor (or PhD) rather than simply inflating titles.