Jared,
When facing Hazards, do you reduce the number of dice rolled by the Hazard Rating, or do you roll your normal dice, and remove a number of dice (highest first) equal to the Hazard Rating?
I'm asking because your text implies the first, but the example implies the latter. If it's the latter, Hazards are a lot worse - a three point Hazard would mean you'd have to spend a Plot Point, then roll 4 dice, dropping the highest 3. Ouch.
Unless I'm insane, the text should say the latter. Every point of Hazard removes a Die Result. Because the Die Result is the highest die, this means Hazards cancel highest dice.
The solution, figure out how to cancel Hazards (through Might and Magic and or roleplaying) or throw lots of dice at the problem.
Also remember that rolling 3 or less doesn't mean you fail, just like rolling 4 or higher doesn't mean you succeed. It could just upgrade or downgrade the toughness of the scene.