We give vaccines to cause the dog to build his own immune response to the disease. So, it is hard to know how much is enough in my opinion. If there was enough of the modified or killed virus in the shot to ensure the puppy's immune system found it, then the small amount should be just as effective as the typical dose. I have not read of any studies looking into this, so the vet may or may not have a scientific grounding for making the choice to use less. I will see if I can find anything!
Also, keep in mind we use the same vaccines for newborn human babies as adults as far as I know.
Experienced with dogs, learning about Chihuahuas!