There are indeed many, many lies, but the Iranian government confirmed these deaths. The BBC is a reasonably reliable source, and if they didn't have confirmation, they'd have written the headline as "Israel claims..."

It's not really much in their interest to lie about killing military leaders, precisely because their goal is to break the spirit. If the guy popped up the next day and said "Nuh uh!" it would be counterproductive to their goal.

For the rest, yes, it's rife with lies. The fact that they are actually killing people does not make this more moral. I'd rather they were lying about that, too.