All the charge action requires is that you move the most direct path towards the target. It does not require that be in a straight line. If that direct path changes due to their actions, it still exists, and you can still continue the action.
I have a "cognitive dissonance" with the most direct path being a non-straight one (i.e. a straight line anywhere from one square to anywhere in another, just like line of effect).
A long curved path might be the same distance, but it is not direct.
For example:
You must choose the most direct path to a target when counting squares for range or when determining the extent of an area of effect.
Do people actually allow PCs to Charge with long curved paths???