One, a placebo does not need to be given blindly. A sugar pill is a placebo, even if the recipient knows about it.
An actual definition: "A placebo is an inactive substance (like a sugar pill) or procedure (like sham surgery) with no intrinsic therapeutic value, designed to look identical to real treatment." No mention of the user's belief.
Two, real hard data proves that the placebo effect remains (albeit reduced) even if the recipient knows about it. It's counter-intuitive, but real.
The hypotheses hinge on the beliefs of the recipients. "The placebo effect" has always been largely psychological. That's the realm of belief.
To veer even further off-tangent, isn't it hilarious how the Wikipedia illustration of old Placebo bottles indicate that "Federal Law Prohibits Dispensing without a Prescription". Wouldn't want some placebo fiend to O.D.