Even a minimalist BC will have a bit more positive buoyancy than a bp/w, but the combined weight of the backplate, webbing and hardware, wing and inflator, and any add ons like a can light combine to nearly equal the weight that came off the belt.
And as the OP suggested, now they are carrying the weight on their shoulders instead of their hips.
If people are overweighted and then shed some lead because they focus on proper weighting due to a switch to a bp/w, then thats great. Its still going to take a specific amount of weight to sink someone who is wearing a 7mm wetsuit and is positively buoyant.
Assume a person is properly weighted with a belt and BCD and then weighs himself on a scale, then switches to a bp/w and removes 10 lbs from the weightbelt and then weighs himself on the same scale, he should weigh about the same, maybe slightly less to counter the tiny amount of positive buoyancy inherent in the bcd.
As mentioned by Akimbo, you can't fool Archimedes.
Yep, that about sums up what most are saying.