Can biological parents falsify information on original birth certificates?

I suppose that its a possibility that it could be falsified. There are however other possibilities for you not being able to find info on them like witness protection or the less glamorous identity theft. The info on your birth certificate that is critical like you birth date, address, and hospital are correct which could give you an idea of your roots based on the general environment even if you can't find any info on your actual birth parents.