As in many other human endeavours competition plays its part in scientific research.
I think you will find that, overall, cooperation is far more important than competition. New discoveries are usually driven by curiosity, rather than by competition. And often the main benefit to the discover is recognition from peers, not riches.
Sure, there are instances where the system has been abused. These usually come to light, and to a large extent the system is self correcting.
As for your hypothetical example, note that people don't just accept theories on the say-so of others. The conclusions will be critically tested by other scientists. By nature, scientists are skeptics.
Let's end the political smears