But saying "they really need to make these doors automatic, I dropped my coffee here last week!" and helping out if they want it has the EXACT opposite effect. Suddenly, it's not embarrassing any more, and you might have a little convo commiserating about what sucks. It's just a little bit of connection to make someone's day a bit better which is definitely a win-win and good way of breaking the seal on talking to folks.
There's also another more neutral option. Just give them the answer they need without the fluff. If they then want to thank you and chat it's their choice, but completely optional.
This is probably not the right approach most of the time, but it works well on the types of people who seem "serious" (not anxious or upset).
This is a really hard one to pull off. You have to determine that they really are that type of person and then just magically know what they want. It's really satisfying when it works though.
I've met some of the most interesting people I've ever known that way.