I think you’ve got the right idea, but may be overthinking it just a tad.
The golden rule is just a proactive step when meeting and dealing with new people. Since you can’t know how others want to be treated from your first interaction, you fall back on the golden rule. So you offer to help someone, they tell you they’d prefer to be left alone, all good. Now you know.
Basically, it’s not just “If I were in this situation, I would want to be helped, so I’m going to keep offering to help.” It’s “If I were in this situation, I would want people to be understanding and gentle, so I’ll listen to what they have to say and, if they ask for help, do whatever they need.”
Where people get caught in the weeds though is often the difference between being “good” and being “nice”, so you’ll never have an objective answer to the best course of action. Just this general guideline to hopefully steer you in the right direction until you can figure the rest out on your own.