When I travel out-of-state I always look for the "state rate" first while booking on-line, this is one of the features that I do like about the Hilton booking site, not all hotel chains offer this option. However, there is no consistancy as to how the state rate is displayed and the qualifiers to get that rate as you have illustrated and I have experienced. Some properties list specifically that you must be an employee of the state in which the hotel is located to qualify. For those I check the rate availability on-line then I call the revenue manager direct before making the reservation, identify myself as an employee of another state and a HH Diamond and ask if they will extend the courtesy of honoring the state rate for my stay. I have been 100% successful when inventory shows available online. For those that don't specifically detail what the qualifiers are then I make the reservation first to secure the inventory then call the reveune manager. In all cases I call the hotel and speak with the revenue manager to secure the room and rate before making my trip. This is no different than seeking special consideration for other perks, i.e. upgrades, additional rooms at discounts, etc. prior to your arrival.
Let's be real, I don't think there are many situations where you don't or can't get differing responses from CSRs and intrepret their published information to your perspective. Bottom line, the real defining point is when and where the transaction actually occurs. I personally would rather know before I travel if I have a firm reservation at a secured rate before I travel.