You're right about the meaning of disinterested. It's impartial, unbiased, or having no stake in the outcome.
If you're uninterested, you're bored, unconcerned, or indifferent. Here's Grammar Girl explaining the differences, if that's helpful.
If you see someone in need and you are not interested in helping them, it is very likely that you are uninterested in helping them, not disinterested. But I think the similarity between the prefixes dis- and un- is what causes people to treat them so interchangeably.
If you look at their meanings, you'll get a better idea as to why disinterested and uninterested are so different yet similar. Basically dis- is used in separation cases, but un- is used for a reversal of an action. It isn't apparent in all cases, but it should help you see why it's so easy to say "uninterested" instead of "disinterested".