The bit about hard drives is true, start up currents on motors are far higher than steady state power draws, large servers can have their drives arranged for "staggered spin up" which means that they start up one at a time rather than resulting in a large power draw all at once.
Your CPU and GPU do not require their peak power, they are running much higher than their idle power levels, but unless you actually have them doing something most of their transistors are sitting there doing nothing and not consuming much power at all. Though for most systems with PSU issues you will find them at startup as it is likely to bring systems that aren't used at maximum load normally to their "peak" power, which is still well below the maximum...