In reply to Josh Grab.

There is a long history of using the predicted response for the X axis in a diagnostic plot. Even for linear models with a continuous response, several diagnostic plots use predicted response as X, including the observed-by-predicted plot and the residual-by-predicted plot. See "An overview of regression diagnostic plots in SAS" for examples. I don't know who first started drawing them like this, but it is used by Belsley, Kuh, and Welsch ("Regression Diagnostics," 1980) and almost certainly by researchers before them. It is a convenient way to visualize models that have multiple explanatory variables. It is also independent of the order of the observations in the data, so doesn't change if you sort the data. Lastly, if you plot observed values as Y and predicted values as X, then the vertical distance between the observed values and the diagonal of the plot is the magnitude of the residual. The graph shows the familiar geometry of least-squares regression.

In a similar way, logistic regression use predicted probability as the X axis for many diagnostic plots. Austin and Steyerberg (2013) have references going back the the 1980s.