The problem is replicators and transporters.
A replicator could fabricate evidence with your fingerprints/DNA and a transporter could plant the evidence anywhere.
In theory a dead body complete with fatal wounds and matching murder weapon could be fabricated and teleported into a place only you can access.
One way to disprove the evidence is with the transporter/replicator logs, assuming they cannot be hacked. This, unfortunately, validates the surveillance state insofar as pervasive logging/accounting can be termed surveillance.
We only get to see the lives of the ship based explorers/soldiers, so maybe things are different in the civilian world.
Like InnocentBystander said, it should still be possible. Internal sensors on federation ships do track everyone constantly, (computer please locate commander data, ect) so they should be able to construct time and place where everyone has been. Sure this is less relevant on a planet especially a frontier world. But they would likely have tracking. The real kings in the world of trek, and tmr are likely those who understand the computers that form the basis of their tech.