I wonder if that it's not an error but a deliberate anachronism to streamline the exposition during the summary. Yes, in some playthroughs the MC didn't tell Sage about his birthday while tending to her - but he did tend to her and he did have a birthday, so it's faster to explain both in one fell swoop.
It would be a bit like playing a voiceover from one scene while a different scene plays in the background; not quite the way it happened but a reasonable approximation. It would certainly explain the more complicated code.
I dunno... if the mc didn't tell Sage about his birthday blues, and Sage didn't feel sorry for him (because he never told her), and the mc didn't even join her on the bed, and then Sage fell asleep while the mc was standing nearby, I think it's just a bug that they showed the "sagePath" outcome in the flashback (Sage falling asleep cuddled in the mc's arms with her teary face).
Also, if you choose Jill, the flashback doesn't touch on his birthday blues, more on the Tybalt blackmail.
Nah, I reckon it's a bug.
I don't know DPC's background, but I don't think coding is his specialty. There are numerous unoptimized implementations throughout the code which can lead to mistakes like this. Typically his play testing is fairly thorough, so they catch these kinds of bugs, but this is an obscure situation; there's probably a low likelihood of a player choosing the Sage visit when not on a Sage path - maybe only M&J purists would do this.
Looking into this scene, I love this bit of dialogue:
Sage: "What are you doing?"
mc: "I was gonna stroke you for a bit."
Sage: "This is not some kind of foreplay, I hope."
mc: "Are you thinking of sex when you're sick?"
Sage: "Like guys aren't thinking about sex constantly?"
mc: "Nope. Not constantly."
mc: "And not when they're taking care of someone who's sick."
Sage: "Why? Because you're caring?"
mc: "No, because it's gross."
Sage: "You're gross!"
mc: "..."
Such a Sage response.
On a side note, the Jill/Sage choice of episode 6 feels like the first time that DPC kinda went formulaic.
Regardless of which girl the mc chooses, he has his whole, "I feel like my birth makes my dad think of my mom's death" dialogue, which gets both girls crying. Choose Jill, Jill cries over the mc's birthday blues, choose Sage, Sage cries over the same story.
Kinda felt lazy to me.
Maybe it was fair enough, it was his birthday, he does feel bad for his dad, so he talked about it with whichever girl he was hanging out with...