Yes that is correct, which is why this debate is always so useless.
Torque and hp are always directly tied to each other by the formula, you cannot increase horsepower at a given rpm without also increasing torque at that rpm.
The only reason torque and rpm are the measured values is because it happens to be convenient to measure those two values. You could just as well use other methods to determine hp and then compute torque.
If you remember your grade school instruction about how James Watt developed the concept of horse power to rate steam engines, he was not measuring the "horses's torque", he was measuring the work they did in specific period of time and that became the definition of a horse power.
1 hp = 33,000 ft/lbs per minute, or 550 ft/lbs per second
Larry