The first place to look to start answering this question is the definition in your policy as to who is an insured. Generally, you will find some wording like this: an insured means you or any relative, or anyone using an insured vehicle within the scope of your permission or within the scope of permission of your adult relative. This does not include a passenger. Upon further inquiry is found the definition of a relative: a person related to you by blood, marriage, or adoption, who is a resident of your household, including a ward or foster child.
It appears under the first definition of you or any relative, it would appear your 16-year-old daughter does have legal standing to loan the vehicle.
The second part of the definition seems to put some limitations on who is an insured and can give permission for someone else to drive. It states within the scope of permission of your adult relative in which case the answer would have to be no.
It would be a good thing to let your child know you don’t want them letting someone else drive your vehicle under any normal circumstances, and let them use as their excuse for not allowing someone else to drive the definition of an insured not covering their friends as found in the policy.
There is a good possibility if the 16-year-old was at fault and caused damage to your vehicle he could be held liable for it, and since he is under age the damages could be assessed against his parents’ policy. These kinds of scenarios are what keeps claims adjusting and litigation so impelling.