It all depends on tone.

If the players challenging the DM is doing so in a constructive tone, which means that the player is trying to make the game world make sense -- the disease example is a good one for that -- then listen and make a ruling.

If the player challenges the DM in a style that is obviously PvP, or "I am right your are wrong" or if there is a bit of pushing/chest thumping going on, the best response I have found in the past goes like this:

1. Pause and say nothing for a moment.
2. Restate the problem or conflict.
3. Ask other players how they see the problem.
4. Make a ruling taking all input into account. (Or, take a break, see below)
5. If the challenger persists or disagrees, take a deep breath and ask the player who the DM is. If the player is there to get into a pissing contest, it will become obvious at this point.
   *At this point, it is time to take a break as immersion is utterly gone if it was ever there.

Break actions:

Get up, get snacks, grab a brew or a soda, take a bathroom break, etc. and either

1. Declare the session over for the night as you need to sort out this conflict before continuing play
2. Declare the session over as you don't need the abuse (this depends on the attitude of who is challenging you). Sometimes, an issue like this does need some time to sort out, and continuing play won't be very productive.
3. Resume play since, during the break, you have puzzled out the problem away from the table and come up with something that resolves the conflict

Note:The question is pretty broad, so the answer can't be much more specific than that.