The battery water or purified water is not necessarily as clean as lab grade distilled water. I know battery waters which have organic content, and I have tested them for the initial wash of argyrotypes, in short they were not suitable. I do not doubt the purity of silver nitrate, even the lowest grade is good enough for alt processes. What you are seeing is precipitation of some silver forming compounds with the materials in water. Filter it and you are good to go with VDB.
Try distilled water next time.