Claire's going through the stones was not accidental, but fated.
Spoiler alert for anyone who hasn't yet read through Dragonfly in Amber… Don't read this post if you don't want to know!
My understanding of time-travel in the Outlander series is that time moves forward, but now and then, a “loop” comes about and is fated to occur. For example, Mary Hawkins was destined to remain virginal until married to a French nobleman. However, Mary was working late at the Paris hospital only because Claire was there, and so, became raped and forced down another path toward Alex Randall. Likewise, because of Claire being at the manor where Mary was staying, Mary did not marry Mr. Isaacson. Because of Claire’s presence in the 18th century, Mary Hawkins would then give birth to Frank’s ancestor, and seal Claire’s destiny in the 20th century.
In other words, if Claire had not gone back in time, Frank would not have existed. If Geillis Duncan had not gone back in time, the money she stole to supporting the 1745/46 rising would not have been available. Without the defeat of the Scots in 1746, Geillis Duncan would have had no reason to travel to the 18th century to try to do something toward the Scots’ success. Her efforts failed in the desired result. History occurred as it was meant to happen. Time works on a loop – certain individuals are destined to go back in time, in order for the fated future to happen.
Notice that Claire’s time travel did not in fact change history, try as she might. The Battle of Culloden still happens with its aftermath. She cannot stop what is fated to occur, and she is actually a part having fate fulfilled. If she really wanted to stop Charles and change history, why not just slip him some cyanide? But she does not.