RMS is .707 of peak for a sine wave that is used in amp testing. Average power is half of peak power. Or, if you multiply Irms and Erms that is .707 of peak, you get half of peak power.
Or, .707 x .707= .5
It also relates to duty cycle. of a sine wave.
Yes, the sources stand and that link stated average power. Simple. Average is not RMS.
Or, the other way from RMS, you multiply it by 1.414 gives you peak. Or, you multiply average power by 2, you also get peak power.
Try it. Google it.
Yes, you can disagree with your source.