No. The concept of random has nothing to do with incomplete information. There are (a few) incomplete information problems wherein one assumes that missing data is "random" (all this is a very loose descripton.) The quantum mechanical description of matter implies that there are "random" (not a-causal, random) events that cannot depend on incomplete information. Quantum mechanics works very well.
There is "Nothing by Chance" - which is the title of a very interesting book by Richard Bach.
Then Mr. Bach's theory of matter must show testable disagreement with quantum mechanics. Ping me when Bach publishes his (refereed) experiments showing where QM fails.
Mr. Bach's conclusion is not based upon matter, it is based upon his father's teaching and his own life experience. His application of this understanding produced a life which I would certainly judge to be successful: Best selling author, pilot extraordinare and owner of all manner of exotic aircraft, cover of Time, married to a former movie star, successful children, etc. An early foundational flying adventure is the subject of his book.
I do not dispute your understanding of quantum mechanics and its relevance to present day science; but I will point out that science is always changing with the accumulation of information, and throughout history what was taken for absolute fact later proved to be illusionary. Which brings us to Richard Bach's best and favorite book, "Illusions". A small book but a great consciousness expanding experience.