Long Live the Confederation!
WC2 doesn’t hint Tolwyn knew Blair. People who knew Blair didn't think he was a Traitor - Paladin flat out tells Tolwyn anyone who served with Blair in the Claw would tell the same.
Then, later, we find out Tolwyn served with Blair on the Claw, and actually knew his character well from WCA. Tolwyn choose to believe Blair was a traitor, just like Paladin chooses not to. Why? Well, Tolwyn didn’t like Blair and Paladin did, that’s pretty much why. The story of WC2 gets even more interesting when you input everything that happened on WCA and the WCM. To think Blair was a traitor, after all that?
In all fairness, no one believed the stories about ghost ships, and Blair's friends considered him merely incompetent. What was more or less what the court decided, since Blair was convicted of negligence, and demoted to Captain. It was Tolwyn who made the decision to end his career and put him on ISS, what was object of much delight for the Kilrathi imperial family.
Tolwyn took a personal interest in Blair's career early on - as far back as while he was still a cadet at the Academy (on Hilthros, that is, not the Wing Commander Academy). Blair was the son of an old comrade, and like his own mentor, Banbridge, Tolwyn firmly believed that the Navy looks after its own. Tolwyn did whatever he could for Blair's career, including grooming him for command and giving him choice assignments on the Tiger's Claw - Blair was learning command tactics from the Admiral himself while his friends were being used as combat ready fighter pilots.
Then Blair betrayed Tolwyn on a personal level - after Dolos he stood up and told Tolwyn off at the Cadet Wing Commander medal ceremony. Tolwyn, an experienced military commander, had no qualms about throwing lives away to achieve a goal... and he almost certainly thought he was doing Blair a great honor by awarding him that command position. In retrospect we can say that young Blair *was* very naive - of course Commodore Tolwyn was going to risk the lives of the men and women under his command to win the war... Colonel Blair would do the same thing many times in later years.
So, going into the destruction of the Tiger's Claw you have that rift. Several other stories also work hard to explain Tolwyn's psychology regarding the stealth fighters specifically. In both Wing Commander Academy and in the dialogue added to Super Wing Commander, we see Tolwyn insisting against all evidence that the Kilrathi can't have developed such a weapon. Why? He claims it's pride in Invisible Enemy. Perhaps he knows that technology is the sole advantage Earth has against the Kilrathi, and that if the Kilrathi deploy something so advanced as invisible ships than that one narrow path to victory is lost.
It might be even simpler than that - in Super Wing Commander he argues tooth and nail against Halcyon that stealth fighters simply don't exist... his pride in Academy (and WC2) may come from this argument alone. (In comparison, we know the military command *did* believe that stealth fighters were in development. The classified document on the Skipper missile in the Confederation Handbook contains a reference to a separate intelligence report on them.)
What makes me think about the ISS. Didn't anyone else who knew Blair - like Paladin - could've helped him? Or didn’t Blair even try?
As you yourself noted, one of the subtlties of Wing Commander II is that when pressed Blair's friends *did* actually believe him incompetant (and thus like the court, responsible in some way for the destruction of the Tiger's Claw). In all likelihood, Gwynedd is exactly where they thought he belonged...