I don't, with a caveat. I think it may depend on the characteristics of the rest of the circuit.
Here's my thinking. Take the very simple case of a PNP transistor with a pull-up resistor on the collector. When you put a high voltage into the base resistor, this creates an active path from the collector to ground through the emitter, and thus the change is, absent anything weird in the remainder of the circuit, going to be function of the characteristics of the transistor, not the remainder of the circuit. However, when you release the voltage on the base resistor, you have shut off the active path to ground and created a passive path back to the supply voltage and thus the response will depend more strongly on the remainder of the circuit because of possible difference between the actions of an active path and a passive path.