What you say is correct for when the pulse is present, but it is not there for 50% of the time. So while the pulse is there it has to delivery double the power, because its going to be missing for the next time period. For example, 12V DC, Vp = Vrms. Now chop this up into a squarewave. So 12V for T, 0V for T, so power delivered = 12^2/R X T + 0^2/R X T, so over a 2T time period, power delivered = 12^2 X T /2T = 12^2/2 i.e. half the power because the 12 V is only there for 50% of the time. So you need 12V X 2^1/2 to make the previous sum = 12^2/R.
Frank