That's how the answer lies in the question itself. As soon as this family had the opportunity to use the official position of head of the family for personal gain, the family immediately "earned" billions of dollars. If it was due to something else, the family would have earned this money even if the head of the family was not the president. Is it logical?

If they just earn those billions from their wide business knowledge and skills, they provably would just earned those amounts even if they are holding a power or not.
But the since after they hold the office their wealth suddenly explore and the family gain lots of power this one shows that everything is not just coincidence, But rather a leverage on their position. This is really straight forward thoughts and we could also see this base on their past also recent action then also on their gains.