Potatoes that have been in proximity to a really bad potato
The general rule with food is: If in doubt, throw it out.

Having said that, hot water is unlikely to kill any bacteria or fungi that came from the rotting potato. Washing will remove most of the contaminants that are on the surface. However - the problem here is that you generally can't see how far a contaminant has penetrated the food that you are eating. For example, in the case of moldy bread - the blue or white bits that sprout out are the fruiting bodies (produce the fungal spores) of the underlying fungus, the actual fungal mass will be many times larger and hidden inside the bread.

It's the same with your potatoes, while you may have removed all the infected bits, you may also not have. Will the infected stuff kill you? Probably not, but it sure won't taste very good and will make everything it is with taste bad too. To avoid wasting all the other ingredients as well as the potatoes, you are best of discarding any you think might be contaminated.

Long story short - throw out the ones that were touching the liquid and rotting potato. The rest should be fine.