History within the bounds of science is surely the only genuine history. That should not be controversial. If perpetual motion machines are scientifically impossible, then claims that one was invented in the past must be rejected.
Does history only within the bounds of science exclude the resurrection of Christ from history? No, since there is no law of physics that says once a person is dead they cannot be resurrected.
Science within the bounds of history is likely controversial. The scientific community resists others except mathematicians telling them what the limits of science are. But if science goes outside the bounds of history, then science becomes a kind of history beyond history.
This is what happens with deep time, the concept of time beyond human history. There are no documents, no artifacts to show that deep time was experienced by anyone. Deep time is disconnected with time as ordinarily experienced; it is in its own world.
Evolutionary and uniformitarian histories are not really histories. The sciences are concerned with all the possibilities of what might happen. If water can take three phases, then a theory of water must cover all three phases. The sciences are also concerned with what always happens. If water freezes at 0º C, then in a theory of water, the freezing point must be 0º C.
But history is concerned with what actually happened in the past, whether it happens repeatedly or is something unique. In fact, to cover the full detail of history, everything that happens must be unique, because the exact same point in time and space will never occur again. History does not cover the full range of possibilities, only those possibilities that are actualized.
Time in evolutionary and uniformitarian histories is theoretical, not actual. The concern is with what might have happened, rather than what actually happened. If it were the latter, then a chronology of events would be developed before proposing a theory. But evolutionary and uniformitarian chronologies are hypothetical, and their histories are pseudo-histories.