I'd like to first of all point out that the first quote you cited is not from any legislature, it is a representation by an author on the website you linked which is dubious at best.
There is a trust fund for vaccine compensation: http://www.hrsa.gov/vaccinecompensation/index.html
"Since the first National Vaccine Injury Compensation (VICP) claims were filed in 1989, 3,278 compensation awards have been made. Over $2.5 billion in compensation awards have been paid to petitioners, and over $100.9 million have been paid to cover attorneys' fees and other legal costs.
To date, 9,620 claims have been dismissed. Of those, 4,229 claimants were paid over $55.0 million to cover attorneys’ fees and other legal costs."
You can gain compensation from a vaccine if you have demonstrably show you have been effected by it. These are extremely rare and only occur in 1 in 100,000-1,000,000, that is why the number of compensations been awarded since 1989 (24 years) is only just over 3000.
This system you describe has been put in place to stop frauds and those who want to take advantage of it.
Millions of people each year receive vaccines, what if a person has a heart attack the day later? Does that imply the vaccine caused the heart attack?
"more than 920,000 Americans will have a heart attack; nearly half of them will occur without prior symptoms or warning signs." which is around 105 heart attacks every single hour.
Think about that when you answer the question above, 105 heart attacks occur every hour. How are we to know the vaccines caused the heart attack?
You'll be glad to hear all you have to show is that there is a 50% chance the vaccine caused your illness or caused your death. The government will give you the benefit of the doubt if you have show this. This obviously implies that many who receive compensation receive the compensation falsely, but it is just how the system goes to benefit those who are affected.
There needs to be a law set in place. There would be tens of thousands of applications each year that would have to be dealt with by the pharmaceutical companies and they simply do not have the time. Tens of thousands of parents each year claim their child received autism from the vaccine yet there simply is no evidence suggesting they did. Autism always arises around the time the vaccines are administered so you can obviously see a causation correlation problem here.