Stating that Vbq6 equals Vcc seems ... incomplete.
But that is not what they say, is it?
You are most likely right that Vbq6 will be lower than Vcc, but any which way you turn it, Vbq6 can never be
higher than Vcc.
For the transistor to conduct, Vbq6 must be at least V
BEQ6 higher than the voltage at the emitter of Q6 (Veq6 for short). So it follows that Veq6 cannot be higher than Vcc-V
BEQ6.
With Q6 fully saturated, there will be a voltage drop of V
CEsat across it, which also detracts from the maximum output. This then gives us VO <= +VCC - VBEQ6 – VSATQ6