And I also think that a secret that big cannot possibly be kept. And when the genie gets let out of that bag, the consequences will just be even worse. Better to be upfront and honest with everyone about the whole deal.
You make a fatal assumption that everyone will accept the truth at face value.
At Narendra 3,A destroyed starship stands as good evidence of our side of events .
With the Xindi,it took the efforts of an inter-temporal agent to reveal the truth.
And Shran's first meeting with Archer wasn't all that happy either.
The Caeliar won't be arround to corroborate our statement,and no culture will accept something outlandish like nearly being wiped out by a MISTAKE without demanding confirmation,or blood.
In the Klingon's case honor law may demand they go to war with the Federation.
And say it does get out.What journalist or alien is gonna ruin their crediblility by suggesting humanity,one of the Borg's favorite victims,was partly is creator?The bar/office/ship security will kick you out ,with a suggestion to lay off the bloodwine next time.