It functions as a trust. If you can get your money back out of it, it is held "in trust" until you ask for it.
That sounds so funny coming from you. You have stated repeatedly that no one will ever get their money back out.
If it was not a trust, then what would one be doing? Donating their money to Pedro's charity?
If someone were to deposit money in the Foundation, then it legally becomes the property of the Foundation. So, in essence, yes they gave it to Pedro. However, the Foundation is not a charity. PPIF's are not even remotely similar to American foundations.