An even better example is that of Picard refusing to provide replacement parts to the Ornarans in "Symbiosis." It's an interesting choice, because it relies on a very direct interpretation of the Prime Directive. To wit: Picard understands that the situation is VERY bad for Ornara and should not be allowed to continue. But rules are rules: he's not allowed to interfere on their behalf, even if they -- indirectly or deliberately -- ask him to. On the other hand, he IS allowed to provide them with spare parts for their ships if they ask him to, since the Prime Directive doesn't actually preclude him engaging in fair trade or rendering assistance to people in need. He can, however, fall back to his "Well, we really can't interfere" justification even if he never actually explains to the Ornarans WHY giving them a plasma coil would constitute interference. They will probably figure it out eventually, and in doing so they will figure out what the Brekkians have been up to all this time. But -- and this is the important part -- they won't figure it out because of anything Starfleet did, and anything they decide to do about the situation will be a result of their own choices, and not choices that were made on their behalf.
And CHOICE is what it all boils down to. Starfleet will help people so long as it doesn't interfere with their right of self determination. Often times, that means helping people in such a way that they don't KNOW they're being helped, so their choices ultimately remain their own and they cannot be said to be influenced by any outside agenda. In the case of Ornara, this is quite a literal thing: refusing to give them the parts for their freighters is easily the most compassionate thing anyone has ever done for those people, but it'll be a generation or two before they figure that out, and in the mean time they're stuck having to clean up their own mess.