Well, not having the book for the larger context there seems to me two possibles at least.
One, this is just another example of a different rules version taking a slightly different approach.
Two, each is true for it's time and source. History is written by the victor, and subject to revision, so the true story could be close to either or both, or different altogether.
Picking apart the quoted bit, and again granted it's out of full context so I may be way off on what the authors intended, I can maybe rationalize both a bit...
"Lorette Kathryn Strider...was selected to command the international crew of StarLeaper One, the first true Terran starship."
OK, two things, in CT the first ship to Barnard was a US Space Force ship only, not international, and it was not a true starship. From this we might infer that StarLeaper One was the first true starship, probably J2* (hence Star rather than Space) to be able to reach Barnard in one jump.
* yes, that's a few years ahead of the "official" time frame but this could be the prototype
"Her mission to Barnard's Star led to first contact with the Vilani. Following the Vilani contact, Strider accepted a position with the United Nations as one of the first envoys to the Imperium."
This further reinforces the idea that her mission to Barnard's Star and first contact was before the StarLeaper One mission. It was after the first US Space Force mission returned that the UN was informed of first contact.
"Strider...was a leading advocate for peace even as the threat of war loomed. In -2408 Strider left
for the Barnard system aboard the American frigate Jefferson, with a last-ditch proposal to avoid conflict. She was too late. The Jefferson was attacked by a Vilani warship and destroyed -- the first major Terran casualty of the First Interstellar War."
This also fits fine with the CT version. The base on Barnard fired on the Vilani merchants. Strider and the Jefferson were sent to avert all out war. They were too late, the Vilani had already sent a warship in response to the incident and it presumed the Jefferson was hostile. So the Jefferson was not the first casualty of the 1st IW, but it was the first Terran casualty, and the first combatant casualty.
Which still begs the question what was the name of the first quasi-J1 ship to reach Barnard under US Space Force command? If it wasn't in fact StarLeaper One and I don't think it was, based mostly on a vague memory of seeing the name somewhere a long time ago. Sounds like an "Ask Avery" question if that section is still active.
Of course the sense I'm getting is still one of "Gredo shot first"
