Can a 'not-so-bright' person do really well (by fluke)? Can a bright person do poorly?
However, the odds of getting them all correct by accident is 1 in 244,140,625 million.
Even getting 8 out of 12 correct are 1 in 390,625.
If someone got a good problem solving score, the overwhelming odds are they got it by solving the questions, not because they guessed correctly over and over.