Although, the more appropriate answer is "Why not?".
There is no evidence to suggest that NPC characters' Pokemon don't know field moves. Just because they're not used against the player doesn't mean they don't know it. For example, there are plenty of NPC characters in places in RSE where you need Surf or some other HM to get to. It would make sense for them to have those field moves, but not actually use it in battle, because with exception of Cut and Flash (*maybe* Rock Smash), the other moves are strong enough to slightly increase the difficulty - which the developers seem adamantly against. Most NPC characters that are not Gym Leaders/E4/ Special trainers are easy to defeat, and to have them use stronger moves like Surf or Waterfall or Fly would up the difficulty. Given the target audience is kids who are probably first timers, it would explain why those moves are not used, and instead a permutation of two useless moves are spammed.
Now, to Sally's specific case:
- Cut is given freely by an overenthusiastic guy in Roxanne city. If you wanted to apply back ground stories to NPCs, it's not too far a stretch to say Sally got her HM from the Cutmaster as well.
- Funnily enough, her Pokemon, Oddish, is one whose leaves on its head are said to be sharp enough to cut down trees.
- In all probability, she doesn't really have Cut (explaining why she's stuck before the first tree). Or does, and is unfortunate enough to battle the player before getting the chance to use it.
- The most likely answer is this, however:
>The usage and requirement of field moves to be somewhere is not stressed upon so much for non-important NPCs. The developers program them to be where they are and little or no backstory is given to the player, because it's irrelevant to the main plot. There's barely any effort made to be consistent with all of the games' mechanics when dealing with non-important NPC characters. Sally just says she needs to use it, as a special message planted by the developers to give a hint to very young (or very stupid) players who don't realise that you need to use the HM Cut to navigate through the Trick House.
EDIT: You're right. It is long but inconclusive. I didn't realize you were thinking in terms of actual coding within the game, and actually checking whether that specific Pokemon had that move coded in. That's not my area at all, and frankly it goes deeper than what I can look for. That said, I did sort of guess it was unnecessarily long (382 words, you say?). Yikes. Poor kid who got banned tho :(
Also, yay! that you don't want me banned xD