Hi,
The Victory Garden was filmed in Massachusetts where the soil is acidic, while ours is base. If you notice, they also used quite a bit of lime that is simply not necessary here.
When I used to be a Master Gardner with U of I Extension, we did not recommend people throwing ash into their gardens. It wasn't going to contribute a thing and it would raise the pH, which wasn't desirable. If you have charcoal briquette ash, then it is not recommended due to the chemicals used to bind the briquettes. I toss my ashes into the garbage.
Regards,