Having Bill for <some department> choose a product to endorse is also 'choosing an algorithm to choose a product'.

Just because your algorithm is a digitally encoded series of steps, as opposed to a a meat-encoded series of steps, doesn't mean you can wash your hands of the responsibility for its outcomes.

If an algorithm told me that the best way for me to optimize my tax bill is to commit tax fraud, I'd be just as liable for it, as if I followed the advice of an accountant to do so. I'm responsible for my outputs, not my inputs.