Jeremy Grantham's work is of course backed by analysis - and this one is of the Statistical kind.

Specifically Mean/Median/Distributional variety of a long cohort ie timeframe of observations.

Said .... you can reproduce this yourself - its not too difficult to obtain daily prices for the DJ-30 from the 1930s. You just have to group the returns by Year and Month - and create another group called Leap ( literally that's what Pres Yrs are): Modulus Remainder( Year) %4 ie Grouping by Y0,Y1,Y2, Y3

What he has done is then break those 2 group MEANS into 2 separate periods and compare. The point is the MEAN is the average of multiple observations ie Years - for almost 100 yrs of observations every 4 year cycle - 25 observations ( 23 I think to be precise based on availability)

So its "NOT PRACTICALLY GUARANTEED" - its the Long term Average - so YES in the long run - the Hypothesis interpretation is as follows:

"Majority of the gains in the US markets are generated between the Fall of Year 2 to Summer of Year 3" ...

It DOESNT MEAN - that every 4 year cycle conforms to the Statistical Mean ie Average - that is contra to the concept of Statistics

Hope this helps!