Wealthy families are able to provide a layer of security that a government stipend never could. You can blow away your monthly stipend from your wealthy family on drugs and alcohol instead of paying the rent, and you're unlikely to end up living on the streets as your family will fold and send you more money. (anecdote: over the last 15 years I've met over a dozen people who were and/or still are like this)
When comparing wealthy family stipends to government stipends, the guarantee needs to be the same. Instead, wealthy families are generally able to guarantee a minimum stipend for their dependents, while governments would be guaranteeing a minimum==maximum stipend for their dependents/recipients.
