While this type of damage can sometimes be cleaned in an ultra sonic cleaner the long term viability of the board can be in question.
If all of the corrosion is not completely removed it can resurface on the board again at a later date.
Think about it like rust on a cars fender. You take the car to the body shop and they sand and remove the rust.
Then the fender is repainted. Everything looks great when you pick the car up, but a few years later you notice little bubbles under the paint again.
Some of the rust remained and now it's back...hmmm