Arrogance: having or revealing an exaggerated sense of one's own importance or abilities.

The mother was not exaggerating the power her sons have.

It see it as a bit of both. More of a 'they arent admitting it, they are bragging about it' type thing.

Instead of judging behavior as honest vs dishonest (a conflict of reason); try implication (if/then)...if few are arrogant; then many are submissive.