The more accurate translation is less able to convey the meaning. It makes less sense as to her being unable to cover up her shame because "to deceive is foolish" as she's blatantly lying that it was nothing. This is one of the cases where a little localization helps instead of hinders.
Nah, disagree. There's no lie, because she's not covering up that she tripped. Which I do think is a poor example for the author to use, because how the fuck would you even lie about just faceplanting in front of everyone? Should have been something like not hiding her stomach grumbling or whatever.
In regards to the family motto change, it takes away from the punchline. Can't lie, shit, gotta confess.