In my opinion, the rectifiers are fine and they are not responsible for the burn spots.You have at least 1 bad rectifier which caused the board to burn on the relay. It will damage the board again and most likely the cell as well. I can not warranty the repair unless you replace the rectifier set.
People get the burned solder joints because of the high amperage and a weak solder point.
I don't know of anyone who had to replace the rectifiers.
I don't see any way that they can diagnose bad rectifiers without having the rectifiers to test.
I don't know why they would even think that the rectifiers caused the problem.
In any case, did you ever try using a telephone type cord plugged into the flow switch plug to see if the No Flow light goes out?
Do not leave the phone cord plugged in. It is only a brief test.
Note that the No Flow light will blink for about 30 seconds when it detects flow.
If the No Flow light is solid, that means that there's no flow.