@Psychronia @jonsmth
Its not just a convenient excuse. The man committed fraud by impersonating a noble, in this case by claiming to have a noble name.
Nobility is conferred by the monarch, and nobles are essentially independent government officials. If the monarch wished so, this can be taken as far as lese majeste (impairing dignity of the monarch), as both this first and second son are essentially proclaiming they are empowered by the monarch when they are not, and THAT can jump straight into treason territory, as in a monarchy the monarch is the state.
So these are actually serious charges, Japan has had similar laws in the past (abolished in 1947), and Mizuha and the author by extension likely know how serious this charge is.
Mizuha probably would've left him off with a warning but given the attitude and the fact that the baron was stripped of his titles for treason, there was no reason to grant clemency for either of them.