BLDC max speed KV or Hz?
You need to consider both frequency and Kv in driving a BLDC motor, and motor drivers differ in how they take this into account. So, both points are correct.

The rotational speed is directly related to the commutation frequency and the pole count. 

And Kv * rotational speed gives you the back-EMF.

If you define the motor speed by generating a fixed frequency, then as JonRB says, you must supply enough voltage to overcome the sum of:
V1 = Kv * actual motor speed
V2 = IR loss from the motor resistance and the torque required to overcome friction and load resistance
V3 = IR loss from the torque required to accelerate the rotor + load if actual speed falls short of driving frequency.

Just as Kv = Speed / Voltage. the torque constant Ki = Torque / Current.

In SI units, Ki is simply 1/Kv : non-SI users have to remember a funny conversion number (which I've forgotten) as well as which of oz, lbs, feet, inches it refers to, or look it up in a textbook.

So, given Kv, you can compute Ki, and therefore V2 and V3 for both components of motor current I.

Driving a BLDC from a fixed frequency, V3 is critical : if the frequency is too high or the supply voltage too low, the motor simply won't start, so it's normal to ramp the frequency up until the desired speed is reached.

Then if the driving voltage is fixed, and higher than V1 + V2 combined, the motor will run, but inefficiently, i.e. waste power at steady state (at constant speed V3 = 0) so for efficient operation you need to reduce driving voltage to V1 + V2 (usually via PWM).

This can get complicated, so most controllers operate as in Bruce's answer : motor speed is controlled by voltage, with the BLDC sensing either the phase of the back-EMF, or motor position separately via hall-effect sensors or rotary encoders, and controlling the commutation frequency to suit the actual speed.