This is true, except amplifiers discharge their power. This means the startup/shut down cycle for them is very hard on them. Like a plasma, the startup is the time when power flows to light the display for the first time.
VCRs, DVD players, cable and sat boxes, they all use a tiny bit more power when on vs. off.
TVs, plasma, LCD, CRT, projectors, amplifiers all use a TON more power and the initial draw of power is very significant. Those are products that should not be power cycled more than necessary and on/off cycles should be considered if it will be more than average.