When looking at your circuit, consider the equilibrium states when output is high, and output is low.
High: Effective 50 kOhm pull-up; 100 kOhm pull-down, so 8V input to +. - would have to go above 8V to turn off.
Low: Effective 100 kOhm pull-up; 50 kOhm pull-down, so 4V input to +. - would have to go below 4V to turn on.
Thus, your calculations seem accurate.
Why would this particular circuit not behave correctly? I don't know exaclty, but maybe the current drive provided by the 100 kOhm resistors is not sufficient. Try 10 kOhm resistors instead. That may still not be enough for properly driving BJT transistors -- 5 mA seems to be a magic place, so perhaps you should actually try 2 kOhm resistors instead of 100 kOhm resistors.
From what I've found, a comparator is just like an opamp, except with worse performance. I'd use a rail-to-rail single-ended opamp rather than a comparator.