The "purge the galaxy" bit was implied later in Voyager to be just a shock-tactic: make yourself sound much more ruthless than you actually are to scare away potential opponents.
At least that's how I rationalise the post-Scorpion retconning of the Undine.
Scorpion Part I
After escaping the first bioship. Kes says what she heard the pilot say:
Kes:...the weak will perish.
When Voyager finds the singularity Species 8479 are using to enter this Universe:
Kes: Yes, I can hear them. They come from a place where they are all alone. Nothing else lives there.....I feel malevolence, a cold hatred, the weak will perish. It's an invasion. They intend on destroying everything.
So it was established in Scorpion Part I that Species 8472 was out to destroy everything, not just the Borg.
So the Borg would have been the lesser of 2 evils. The Borg had already destroyed hope of diplomacy by invading their space. Picard would have had no choice.
I know, that's exactly what I was adressing: as shown later in VOY, the Undine don't really want to annihilate all life in non-fluidic Space, they're just trying to (and succeeding) scare the opponent shitless.
And Picard wouldn't act on premonitions/visions of his empath/telepath alone.
He'd take it into consideration, but wouldn't base his whole policy towards a new species on a 3-second waking dream of Troi's.
What seems to be the deciding factor for Janeway is the attack on Kim; which is a purely emotional response, not rational given how quickly it happened, where it happened and all they ignored about the Undine.
Kes' vision establishes that they're alone in fluidic space, so the only humanoids they ever saw by that point were Borg, that Undine finds a bunch of humanoids on a Borg vessel and lashes out, in pretty poor lighting conditions nonetheless.