The key is to set initialValues = NA in rxLogit().
For rxLogit, initialValues defaults to NULL. From the help for rxLogit: "The initial values will be estimated based on a linear regression. This can speed up convergence significantly in many cases. If the model fails to converge using these values, estimation is automatically re-started using the NA option for the initial values." If NA is used, "Initial values of the parameters are computed by a weighted least squares step". For rxGlm, initialValues defaults to NA.
So if the results from rxLogit are unexpectedly different, it may be that the model does converge with initialValues=NULL and the function returns different results. When running the example with initalValues=NA in the rxLogit(), all results match.