Hi jcampbell-smith,
I can certainly see how that might seem confusing! JMP is not plotting incorrectly though, but is rather plotting something different, and importantly, generalizable to plots for more complicated logistic models. In your example above, any observation above the line is a "yes" response, and any observation below the line is a "no" response. The location of the points in X space reflects what was measured for that observation, but the exact location in Y space, other than being above or below the line, is arbitrary. This last point is important… JMP is space-filling to convey in a very visual way where observations are, and how the probability of being above or below the line (answering Yes or No) depends on your X. The line partitioning the area is showing the probability of a "no" response at a given X value. As you can see, the probability of a yes response is decreasing (no response increasing) as you increase X since you can see there are far fewer Y responses above the line at higher values of X, and many more values above the line at low values for X, something that is very hard to see without the jittering within each space (as is done in R or other software).
For more information, here is the basic documentation on the logistic report:
The Logistic Report
and here are some additional examples:
Additional Examples of Logistic Regression
In the second link you will see some examples with ordinal and multinomial logistic regression, something I haven't seen another piece of software display well graphically.
e.g.:
I hope this helps!
Julian