This is an excellent question.
To answer how you'd add backup for something "obvious," I'd like to walk you through my writing process when answering a question on IPS. It usually looks like:
- Read the question.
- Be struck with inspiration to give certain advice.
- Write the advice: "Do this!"
- Ask myself, why am I suggesting this advice? Why do I think that this will work?
- Explain both of those why's, giving the logic behind the advice.
- Ask myself, where did I get that logic? How do I know this?
- Either explain the/a situation(s) that taught me this or google around for an article explaining the basic concept.
For that answer, the advice may start as:
Simply ask them! Try: "Do you mind if I fill my drink?"
The "why" may be (taking a total stab in the dark on this, but let's assume this could be a valid choice of logic behind the answer):
When in a situation where some people may be comfortable with you taking an action and other people may react poorly, a simple solution is to ask! The worst thing that can happen is that you receive a "no." Specifically with strangers, it's always better to err on the side of caution and ask permission rather than assume.
And now it comes down to why did you think of that as your logic? For you, you could cite that you were taught to always be kind to strangers and ask permission before doing things that may upset them from your mother--and that would be perfectly valid backup.
If you wanted to be a superstar, or didn't have your mother's advice on this, you could also talk about a situation or two where you used that advice and it worked well for you. Or maybe you could google around for articles concerning asking permission and strangers to see if you could find an external source.1
Note that even if your advice feels "obvious" to you, it may not be to everyone! Pulling apart your logic and self-reflecting on your own answer is hard. But by giving us this insight into your thought process, you build stronger answers and help us all improve our interpersonal skills by giving us a set of logic we can apply to other situations as well :)
1. After googling that myself, I've found pages and pages of articles about asking strangers if you can pet their dog. If I were writing this answer and didn't have any personal experience backup, I'd take those dog articles and run with them! I'd relate wanting to use the drink dispenser at the same time with petting a stranger's dog (in both cases they may be extremely offended or they may be happy to share). And then I'd quote some advice from those articles. Just because you can't find an article directly related to the situation, doesn't mean you can't get creative!