I asked the same question in another forum and got the following explanation. These are not my words, but those of a gentleman that is very familiar with grafting.
"Bark grafting is done when the rootstock is in full leaf and the sap is running. Normally we start just after full leaf-out. A scion has a certain amount of stored energy in it. Take a dormant persimmon scion and place it in medium and try to start it like you would an elderberry or other cutting. Watch what happens. When it is warm and gets enough light, it thinks it is spring and the buds start to open. It will leaf out and look great. You will think you have success and then it will die. Unlike many other trees persimmon are notoriously hard to root. The reason it dies is there is no root system to support it. The reason it lived so long is that it used the energy stored in the scion itself to push open those leaves.
Now think about bark grafting. You are trying to get the cambium layer of the rootstock to bond with the cambium layer of the scion. This takes time. You need good cambium to cambium contact and good pressure with bark grafting as well, but it still takes time. Until that happens, they scion needs to survive on the energy stored in it. If you start with a scion that is not dormant, much of the stored energy was used to break dormancy. So, the scion has less stored energy and thus less time for the cambium bond to take place so it can be fed from the root system.
Will it work to take scions late? Sure, often it will work. But if you want to maximize your chances of success, you should start with a dormant scion.
Having said that, there is a balance. Once you cut a scion from the tree it begins to degrade. We try to delay that degradation by keeping it just above freezing with the right humidity so it does not dry out or get moldy. However, the longer you keep a scion, the greater the chance of one of these conditions making it non-viable.
So, the best time to take a scion is at the last minute when it is still dormant before the buds begin to swell. However, that is too early to bark graft because bark grafting requires the sap to be running in the rootstock.
My guess your gentleman friend probably does cleft grafting or a similar technique that is done when both scion and rootstock are dormant. In this case, you can take a scion from a tree and walk to the next tree and graft it. However, read some of Phil's posts. He did a bunch of persimmon grafting this year. He started early doing cleft grafts and then later did bark grafting.
If you are an experienced grafter you may have good success with cleft grafting. However, if you are just starting out, I'd recommend bark grafting."