Nope, look at the current flow from base to 5V supply - it's modelled the reverse leakage current of the LED. This is the point where modelling with idealised circuit models will give you a somewhat distorted view of reality, the Vce of 6-7mV (on state) will be... unusually low. Similarly the reverse bias current flow through the LED will be highly variable during manufacture and you're likely to see Vc vary quite wildly with component selection and temperature. But the principle of the simulation is correct and shows that the OP pretty much got a workable solution - with the addition of a diode to limit the reverse-bias current flow through the LED. Of course, with this making the 21st post on the subject it would be quicker to breadboard the sucker and just test it :)

EDIT: Dammit - that was looking at new posts and believing post#20 was the latest.