Do you think the U.S.A over reacted in this case, rest in details?

The a few weeks ago a french girl (19) was visiting her mother who lived in B.C.
The French tourist went for a jog on the beach, and accidentally wondered into the u.s no signs or anything pointing out the border, she was detained by U.S.A border patrols and questioned for 2 weeks.
The border on the beach is not marked with any signs, and crossing without authorization is illegal, (I get that).
But to to keep her for 2 weeks is ridiculous.
I think they could have found out this was an accident, maybe fined her and been done with it in a few hours.
What is your opinion?