Question for those in favor of Picard's actions- if the Baku had bottled up the particles themselves (as opposed to settling on the planet they orbit), used them only to benefit themselves, and would not share them, would you still be sympathetic to their supposed plight?
Because it seems to me that that's effectively what's going on here - the Baku have access to a technology that could be used to help others' suffering and will not share it.
The "they were never asked to share it" argument is bollocks because even if they were never asked previously they certainly become aware of the situation during the events of the film. And if we're going to look at this from a moral standpoint, morally I think it's quite acceptable to offer to help suffering people rather than waiting for them to ask you.
In short I believe this boils down to either weak writing or the Baku not being the type of people the Feds should necessarily be setting out to defend.