Despite a few hiccups, I still enjoy this episode, for several reasons, not the least of which is a TWoK reunion of Judson Scott & Merritt Butrick, both doing wonderful jobs with their new characters.
On the dilemma, I'd say Picard was both right & wrong. In refusing the coils, he's right that it's cultural interference. Had the D not been there, the Ornaran ship would've been destroyed, & the faltering of those 2 cultures' socio-economic status-quo would've already begun. Only through the happenstance of the D responding was it averted. In order to minimize the effects of interference, you limit your aid, much like he did.
Where he's wrong is that in responding to the distress signal, and saving the Ornarans, he's already rendering aid, which in itself is interference, that I assume we all agree is rightful. However, when they claim to have a plague, it becomes a contagion protocol (admittedly TNG is very naive on bringing unknown biologicals aboard)
Once they admitted the Ornarans to their medical treatment, & Crusher began diagnostics, with the intent to discover and possibly treat the illness' infected, they took on certain medical responsibilities.
She even allows them to take their own "Medicine" under her supervision, monitoring its effects. At this point, they are knowingly under her professional care, & medical ethics demand that any ministrations she's provided or permitted, diagnoses/treatments she's determined, or information pertinent to wit, is all binding to divulge to the patients, despite the Brekkians wanting it withheld. That interference is already damage done, when choosing to respond to distress signals this way. To withhold it is playing God on them and violating medical ethics. Hell, half the parties were already told anyhow.
You tell them they aren't fatally sick, & give them the info about the nature of their symptoms. You then broker the most peaceful & efficient situation to rid yourself of them & their issues, giving them nothing else, taking them nowhere. I wouldn't have even helped deliver them & their shipment.
Send a ship, dipshits, & take a hike. Work this shit out yourselves. If you come to some compromise among yourselves, and contact us together, asking for aid, I'll submit the request through the proper channels & the UFP can determine if they will do so... but today? You're gonna stop getting your shit on my shoes, just because I was kind enough to save your sorry asses.