Yes. Agree with everything (except "How many jelly beans fit in a car?" - fatuous).
I have met some HR teams that add value, but not many. I worked for one company that employed over 90,000 people without one HR person. It wasn't perfect I have to admit, but when the new CEO started them, things got worse instead of better.
Oh and here's what I think about those smart-arsed interview questions: http://corporatehandyman.co.uk/for-companies/smart-arsed-interview-questions-were-never-ever-big-and-clever