I have done all 3 of the OPs scenarios many, many times (1 & 2 for business, 3 for personal travel). My company uses Amex for corp travel, and I book most of my stays on the website (what used to be called RezPort), but somethimes my admin does it over the phone if part of a complex itin.

In EVERY case I have gotten points. That includes very deeply discounted amex rates - eg CP LHR @ GBP 60 14 day adv purch non-cxl (often half the best rate on the website) which I book several times per year, and also special corp negotiated rates at other properties, which are often even less than half the best rate available on the website.

I know that technically deeply discounted may not qualify, but I personally have never seen it happen. It looks like you were unlucky (or maybe I am unbelieveably lucky - but I'm talking about 50+ stays over the last couple of years, so that seems very unlikely).