Perhaps. In my experience (in the US), your regular vehicle coverage extends to a rental. I called my carrier to double check since I'll have this rental long term. I was assured it's just like driving my own vehicle with same deductibles, etc.
In BC, the government has an arm's length agency that we're required to insure through, our only option. They're the ones that said only if we have the extra (optional) coverage, not otherwise. As it happens, I do have that, and perhaps coverage through my credit card company too (not sure, if I'm not paying for it). The guy here was definitely unconcerned, yes, saying the issue of concern hasn't happened in Canada, therefore everyone's fine, not to worry about it, and just get my new part in some months.
I'm just finding it fascinating, the response you guys are getting and the response here.
Yes, out of curiousity I will call another dealer. This was the same one that, after I told them a light was out and left the car with them for three hours, gave me back a car with a light out... They said they looked and it was fine. I turned my car on and showed them: no light.