The way I read it, it says "Early check-in or late check-out upon request for Eligible Stays.6" and in footnotes only that eligible stay means the Elite member needs to be the registered guest and that early check-in and late check-out means 2 hours prior or after the standard time.

Nothing about the benefit being at the property's discretion, so the publicised benefit should apply in all cases and it should be up to the hotel to make sure they can deliver it, as it's part of the package, so to speak.

Otherwise, it would be like pre-paying for a breakfest inclusive rate and then the hotel telling you at breakfast time that their restaurant is actually closed.