Why do we believe it? When we attend a meeting; just right after we leave the meeting room, every one understands the conclusions of the meeting differently. Even if it is written, every one interprets the message of the written message differently.

In politic, people distort messages for their favor, even when the message is recorded, the interpretation can be quiet different.

How do we believe in the ancient Tipitaka whether it is genuine or altered. We don't know the real teaching of lord Buddha. We believe what we believe as we interpret things on our own favor. We have our own versions of Buddhism that fit ourselves. Each of us has our own version of religion.
It should be verified through pratice by what you experience at the experiential level. If you experience something you know for a fact it is true. 

Normal you should:


Learn the theory (Pariyatti)
Practice what you learned (Patipatti)
Experience what you learned why which you verify the teachings (Pativedha)


When you reach 3 your doubts will be cleared as you know for yourself.