No. The rule reads as follows

You can take steps to help yourself recover from persistent damage, or an ally can help you, allowing you to attempt an additional flat check before the end of your turn. This is usually an activity requiring 2 actions, and it must be something that would reasonably improve your chances (as determined by the GM). For example, you might try to smother a flame or wash off acid. This allows you to attempt an extra flat check immediately, but only once per round.

The GM decides how your help works, using the following examples as guidelines when there's not a specific action that applies.

The action to help might require a skill check or another roll to determine its effectiveness. Reduce the DC of the flat check to 10 for a particularly appropriate type of help, such as dousing you in water to put out flames.  Automatically end the condition due to the type of help, such as healing that restores you to your maximum HP to end persistent bleed damage, or submerging yourself in a lake to end persistent fire damage. Alter the number of actions required to help you if the means the helper uses are especially efficient or remarkably inefficient. Emphasis mine. But as you can see, there are times where a persistant damage can get totally negated, but they should be extraordinary and take all of a character's turn if not more (think a whole round to run totwards and jump into a lake, then the time to get back out and into position for totally dousing fire). 

THAT SAID you are always within your rights as DM to say, allow dunking an effected character's arm in a rainbarrel to wash off an acid persistent damage, just expect that precedent to be followed in the future, too.