They're not back-to-back missions (it's missions 4 and 6/7 we're talking about), but yeah, I imagine that had anybody really thought about it, they could've figured it out - Spoons certainly did. I haven't really thought about how Bradshaw got away with it, but I suppose there's a few possibilities that you can choose from:
1. It simply didn't occur to anyone. Bradshaw was a good officer and all, and certainly there was no reason to suspect him of being involved with the pirates. It's hard to find something you're not looking for, even if it's in plain sight.
2. If Bradshaw flew the Sabre, it might not have had the flight recorder switched on in the first place - it had only just been salvaged from the station, and all the techs had time to do is fuel her up.
3. Jean (the tech) figured it out - and helped Bradshaw cover it up, since he'd just rescued her brother (...was he a hostage, or a defector?), after all.
4. The incident was reported, but either the Captain or somebody even higher up decided to cover it up. I doubt this would have happened out of sympathy (everybody understood the defecting pilots' anger - but since Confed crewmen died during the raid, there would have been no sympathy as such), but... we do know that if you don't cover for Sparrow, she still gets off the hook somehow (and Squealer, for whom you cannot cover in the first place, gets off the hook anyhow). Heck, if you don't cover for Sparrow, Bradshaw notes that one thing they didn't charge her with was treason. It's likely the whole thing was swept under the rug because of how embarassing it was (pirates, robbing a carrier!), and because the Kilrathi could have used the incident to force even faster disarmament. After all, if Confed pilots can turn to piracy at a moment's notice...
And no, no one of these explanations is "official", whatever that would mean with a fan project; we don't need to decide what really happened out there, so we're quite happy to leave it to everyone to interpret as they like. However, one thing is certain - whether or not Bradshaw's sabotage was detected and reported, some covering-up further on in the chain of command must have taken place, since otherwise, there's no way Squealer (and Sparrow) could have avoided getting executed for treason.
(so how does this fit with Bradshaw facing execution if
he defects? Good question
)