Even in a UBI setup, it's the government's/public's money, not the recipient's, right up until the point where it changes hands. A wealthy family can (and often does) make just as strong of a guarantee for a stipend as a government can.
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.
I'm advocating for turning anecdotes such as this into data by actually performing a study.
It appears you're referring to when I said "(assuming a highly controlled, completely reproducible experiment actually can be set up in social/economic sciences)". I'm not making this assumption, I'm questioning if a meaningful experiment can actually be formulated and performed.
If a meaningful experiment can not be performed (and I'm not saying that it can), then examining and observing how people born into rich families operate would give better, or at least no worse, information than an uncontrolled, non-reproducible experiment would. And it might actually be cheaper to study those with money already rather than give people money just to be able to study them.