I am unwilling to accept it because is it just some bullshit you made up as opposed to being an actual fact.yet again you try to conflate "fair trial" with "rule of LAW". It's a court of Law, not of Justice. But that's something you seem unwilling to accept.
This is a definition of the rule of law "the restriction of the arbitrary exercise of power by subordinating it to well-defined and established laws.". The rules around a fair trial (to include the right to legal representation) is one of the restrictions of the arbitrary exercise of power.
The terms "court of law" and "court of justice" are largely interchangeable in common usage. There is a difference between them (but not the one you think). In a court of justice the Judge alone delivers the verdict. In a court of law it is a judge and jury who deliver the verdict.