There is nothing inherent in Quantum Theory which requires randomness. In the 1950s, Bohm developed a deterministic non-local theory which is consistent with all the predictions of quantum mechanics. It is legitimate to draw general conclusions from consistent observations. No influence propagates faster than the speed of light. The third condition would prevent causality being violated, and make the theory consistent with Special Relativity.
Some scientists claim that quantum theory necessarily requires faster than light influence.
In 1964 J.S. Bell devised a mathematical inequality which, if it were violated by experimental data, would demonstrate that the locally realistic view of the world was false, but that quantum theory was still valid and might be complete. So far all experiments have been consistent with quantum mechanics, but not conclusive. Alain Aspect's experiment in 1982 was thought to be conclusive, but subsequent analysis has revealed some weaknesses with the experiment. To summarize, it has not yet been conclusively proven that quantum theory is necessarily random, or that a more complete theory involving additional variables is impossible. Any more complete theory will almost certainly be radically different from the existing theory.