No, they don't "know".
Those symmetries are not shown to be universally true, they are just what we have been able to observe, much like Newton's laws are based on observations on the Earth only.
Yet Einstein showed that they are only a special case of a much more general universe.
It's possible that you didn't read my comment carefully enough.
I wrote: "Physicists knows the exact reason why energy is conserved and why it might not be conserved."
To parse it:
1. exact reason why energy is conserved
2. why it might not be conserved.
Physicists knows the exact reason why energy is conserved and why it might not be conserved. Conserved quantities arise from symmetries in variational systems. Conservation laws are consequence, not unexplained axiomatic law.