Sorry to hear the mishap. You can always try the warranty route, but with all the rust you described, the odd is they will likely know it has been filled with water.
According to the warranty term: “ The warranty does not cover manuals, fuses, disposable batteries, damage from neglect, misuse, contamination, alteration, accident or abnormal conditions of operation or handling, including failures caused by use outside of the product's specifications, or normal wear and tear of mechanical components. This warranty covers the original purchaser only and is not transferable. ”
So they have numerous reasons on why this is not a warranty claim but a billable repair. It will be up to them to decide what they would want to do. Before paying for all the shipping and possible repair bill, I would try the suggested repair first and see if it helps, you have nothing to lose.
With regard to whether it will ever be a safe DMM after the repair, there are just too many variables and potential points of failure. Your only safe bet is to send it back to Fluke for a full repair if you are worried about it.