I don't have to know how something is done for it to be worth paying to have it done.
I'm not sure freedom is what one gives up in this situation. It seems more like giving up control. And one has to do that in life just to be able to delegate tasks to others.
Is it really freedom being given up or freedom obtained by freeing up one's time to do things you value more than examining the code for the microprocessor that makes your clock radio work?
And its freedom that makes it possible for one person to offer the work of their minds to others without having to disclose everything about how it is that they are capable of doing it.
We are free to make such a deal and then later if we choose another alternative. There is no loss of freedom at any point, just the exercise of one's freedom.