Fresh differential fluid improves MPG?

Not trying to diss this guy but could he be right about changing out the differential fluid to improve his miles per gallon? I know new engines have "break-in" oil that needs to be changed but does the same go for factory filled differentials?

https://www.youtube.com/watch?v=T0uWH2vfjJ4

 

Break-in fluids do just that - collect metal shavings, assembly lube, particulates etc. during the break-in process. Don't think it has any effect on mileage.

 

I picked 1 mpg on my 2007 FJ Cruiser when I changed out the rear diff oil at around 70,000 miles.

 

I just had a transmission fluid drain and fill done, gained .6 mpg.
I was like a kid on Christmas morning haha