Sure. The final response from them was (verbatim except for changed names and clarifications I added in brackets):
I am so sorry that this question has turned into a headache. We have gotten a few different answers from a few different underwriters, and the one from yesterday definitely gave us the wrong answer for Oregon. We do not require [your partner] to be registered for the coverage to extend seamlessly to a car you or her rent. She can be second or first named and it is the same. I don’t know how they gave so many different answers other than some states have different requirements, but Oregon policies are good to go without [her] being a registered owner [on the vehicle registration]. I called again today and spoke with an executive senior underwriter to let them know we have gotten several conflicting answers, and he confirmed we are correct that [she] and you are both covered under the extended coverage from the [car insured under your policy].
I even had him notate the account since it has been back and forth, again I am so sorry for the inconvenience of you having to keep checking. One thing to note, if you are going to rent a car for more than 30 days in a year then there is a small endorsement we want to add that acknowledges we are extending coverage to a non-owned car for more than a simple vacation for example.
You’d think, right? But apparently half the company doesn’t know that either 
I didn’t think they were trying to give me the runaround on purpose. It was probably just run of the mill bureaucratic incompetence of the sort @ParallelLines was familiar with.
In fact State Farm has been very good to us, having reimbursed a bike theft, a rear-end crash that destroyed some expensive bikes, and arson that destroyed our other car. Despite all that, they haven’t raised our premiums or dropped us.
I wasn’t trying to set them up for failure, lol, I was just trying to get an answer to what I thought would be a straightforward question.
Apparently so! Every time I sign up for a policy, it feels a bit like gambling at the casino… except I don’t even know which game I’m playing or how much money I’m betting. The only thing more confusing to me is US healthcare policy. (Not going there in this thread!)