This is actually pretty plausible. In the United States, we're used to thinking of adoption as something people do out of their own good hearts or when they cannot have a child themselves. In Japan, however, adoption is more of something more high-class people do when they feel that the heir they do have is incompetent, or they haven't been able to get one for whatever reason - in Giovanni's case it might be lack of a wife. It might be that Silver is biologically Ariana's son and was adopted by Giovanni as his to inherit Team Rocket.Although I doubt the games will ever explore this in detail. 
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