I don't want to sound like a gun nut but this is hardly a "backfire." It's been legally verified that it's perfectly acceptable for citizens to buy guns in this manner. I argue that regardless of whether a gun is bought by the police or bought by someone else, the goal is still achieved: a weapon is moved out of an environment in which it is unwanted, potentially unused and hazardous, and into one in which it (hopefully) will be handled respectfully and safely.
Plus, despite the official politically correct and sensitive statements, gun buyback programs are very clearly intended to reduce the pool of guns available to people who are statistically more likely to use them for nefarious purposes. When someone brings a rare and special piece, you can bet the police will keep it as a memento just as much as any private collector or businessperson. It's those special pieces that these interlopers seek to purchase. All the usual gang-banger favorites and such end up going where they are intended anyway: into the furnace.