How was the Annie doing?
The fundamental question is, "What is the opportunity cost of buying one item over another at any given point in time?" Rod of Ages is a core item on certain champions, and Hourglass is staple on almost all of them. So for these mages, the question ultimately isn't whether or not TO buy these items, but WHEN to buy these items. In Annie's case, it may be possible she wasn't being harassed that much by Zed and didn't particularly need the armour. Or perhaps with her E, she was able to avoid enough of Zed's ultimate damage that she didn't need to rush a Zhonya's. More likely, however, Annie players would save their stun for when Zed ulted and immediately counter-engage on them. In this situation, the stun needs to come out immediately when Zed reappears from his ult. An Hourglass active lasts two seconds, and by that point Zed has already retreated back to his shadow.
There are two main aspects when choosing which item to buy in what order: a) survivability, and b) aggression.
Let's talk about survivability. You're in lane and you KNOW they're very aggressive or pushing you fairly hard. In this situation, you simply buy what is causing the most trouble for you. If you're Diana getting harassed by Orianna, get an Abyssal Scepter to nullify a lot of her damage while still giving you enough output. If you're Fizz and the enemy Yasuo is pressuring you, rush the Hourglass before the Lich Bane. It doesn't mean abandoning your core items, but build according to what you need to live.
Second is aggression. Now YOU are the one pressuring the enemy. What do you need to penetrate through THEIR items that they've bought to negate YOUR damage? Stacking MR? Buy a Void Staff. Are they simply building health against you? Grab a Deathcap.
After your core is bought (in the order necessary for your situation), the final items that guides say are "situational" are strictly that - you buy whatever you want, preferably what helps you most.