Spoiler
Show
The Loroi are on the up and up, and it really was shot down by the Umiak. The Barsam comment about the "lies" the Loroi have been telling merely refers to how they've been claiming they're direct descendants from the (most recent) Precurser race, when it looks much more likely said precurser race merely modified humans to create the Loroi. But why is the Historian personality construct so adamant that the Loroi do not have his best interests at heart?
The Loroi shot down the Bellarmine, and pinned it on the Umiak. They've actually got a pretty good justification for this: the Umiak are using Farsensor cloaking technology, and then a similarly 'cloaked' ship appears next to them, so they shot it down... but it wasn't Umiak at all, it was Human. Oops. And we actually get a glimpse of the enemy ship on the Bellarmine monitors, and it looks a lot more like a Loroi ship than an Umiak one. But then why would they be so thorough in completely wiping out the ship, when logically they'd want to make sure the cloaking technology was intact so they could study it. And if they were trying to wipe out the humans, it doesn't make much sense to then spare Alex and formally recognize him in front of alien witnesses. They could be trying to manipulate humanity... but why bother, with a race so inferior to themselves and their allies? Maybe there are multiple factions in the Loroi fleet, with conflicting goals.... (On that note, we've only got Loroi word that Alex was the only survivor...)
The Bellarmine was shot down by a third party trying to escalate conflict. This same third party would presumably be responsible for the mysterious incident that kicked off the whole war. Honestly, I'm probably just paranoid from my experience with the Lost Fleet series... but just because I'm paranoid doesn't mean the idea is wrong. This would explain the effort they went to to eliminate any witnesses.