^That was Admiral Nora Satie. I completely forgot about her, which surprises me because "The Drumhead" is one of my favorite TNG episodes. I don't think she was incompetent so much as she was nuts. She saw conspiracies everywhere and wasted valuable time and resources persecuting people who'd committed only marginal offenses.
I mean, who really cares that Simon Tarses lied about his heritage? Did his being Romulan as opposed to Vulcan have any bearing on his status as a member of Starfleet? It's not as though he was spying for the Romulans. His grandfather was Romulan, which tells us little or nothing about what kind of people Simon was. I suppose his dishonestly could have called into question how trustworthy or reliable he was, but given the way Romulans were themselves perceived in the Federation, it's not hard to understand why he'd have hid his background.
As an aside, it would be interesting to know the circumstances behind his grandfather conceiving a child with a human woman, but that's hardly relevant in terms of Simon's place in the Federation.