YARN
Fleet Captain
The Eminiar were the 2nd party, obviously, and escalated the situation to conflict level by declaring their intent to take the Enterprise and murder the entire crew.
LOL, by "2nd party" I though you meant a space-faring outside party (like Klingons hiding in the bushes, which usually allows for bending the prime directive).
In The Corbomite Maneuver they encounter a warning buoy, destroy it, and then press on ahead into that sector anyhow.
In Requiem for Methusela it goes like this:
KIRK: Let's get that ryetalyn.
(A strange device comes travelling through the air towards them. A bit like Nomad, but much smaller and with more round bits. It fires an energy beam at the landing party's feet. They try to fire their phasers.)
KIRK: Inoperative.
(The device fires again, and closes in.)
FLINT: Do not kill.
(The device backs away and a silver-haired man in sort of doublet and hose approaches)
KIRK: I'm Captain James Kirk
FLINT: I know who you are. I have monitored your ship since it entered this system.
KIRK: Then if you know who we are, you know why we're here, Mister?
FLINT: Flint. You will leave my planet.
SPOCK: Did you say your planet, sir?
FLINT: My retreat from the unpleasantness of life on Earth, and the company of people.
KIRK: Mister Flint, I have a sick crew up there. We can't possibly reach another planet in time. You can't refuse us the ryetalyn.
FLINT: You're trespassing, Captain.
KIRK: We're in need! We'll pay for it, work for it, trade for it. FLINT: You have nothing I want.
KIRK: But you have the ryetalyn that we need! If necessary, we'll take it.
From here Kirk proceeds to attempt to steal the affections of Flint's fembot, resulting in the death of an artificial life form.
How was this situation in any way precipitated by Starfleet?
The Eminarians specifically ordered/warned Starfleet not to visit them. They did so anyway and became subject to their jurisdiction, which they promptly refused as soon as it became inconvenient.