>I ask this as a layman, and I'm really interested if anyone has insight into this.
Another comment basically answered but basically you are touching on Hidden Variable Theorems in QM. Basically that there could be missing variables we can't currently measure that explain the seeming randomness of QM. Various tests have shown and most Physicists agree that Hidden Variables are very unlikely at this point.
Local hidden variables are impossible. Non-local hidden variables are perfectly possible. Aesthetically displeasing, since it requires giving up on locality, but not logically impossible. Non-local interpretations of quantum mechanics give up on locality instead of giving up on hidden variables. You can't have both, but either one alone is possible.