Good guess! I did know this.
Note that he didn't need to identify which specific bacteria was causing the infections. He needed to know which well to remediate and that chlorine would remediate it.
If he decided not to chlorinate the well in order to fully decide which specific bacteria was causing cholera, that would have been stupid.
The additional information would not have been worth the cost of acquiring it.
It would not have changed anything about the correct remediations and it would have incurred significant cost to acquire that information.
Great analogy, to my point :)