Backcourt Violation?

[Adam]

B touched the ball in the front court.
A then touches the ball in the back court. The ball cannot have fc and bc status simultaneously, so as soon as A touches it it has bc status.
No violation, as A was not the last to touch in the front court. The rule says nothing about causing the ball to gain a certain status; it only mentions first to touch, last to touch, etc.
No written rule has been broken.