Whether they were "technically working" is a matter of interpretation.
I don't think I'd buy that, but accepting that judgment for the purpose of discussion, if you are going to take the average wage approach, you need to figure in the non-wage compensation: Shelter, food, medical care, and perhaps other non-wage benefits.

Now, taking your figure of $5.20 for the moment, is it taxable as income? If not, then one would have to figure what amount would be equivalent if it were taxable.

There's also the value of the possibility of winning the $20,000.

Considering all the above, it would definitely be above the minimum wage.

You can also consider this as being a species of vacation, which complicates such an analysis.

Dave Oesterreich