Why does the current not flow directly to ground?
The only thing I can see is if the combined voltage drop across Q1 C-E and Q2 C-E if they were to conduct is larger than the combined voltage drop across R2, Q3 B-E, and Q4 B-E.
Then Q1 and Q2 would fail to divert current flowing through R1 away from Q3's base and be unable to keep it off.
You can probe your circuit voltages to check but won't be able to directly measure Q1 and Q2 as is if they are not conducting. You would need to open up R2 and so that they are conducting and compare.