The pickers in my neighborhood are a nuisance. If my recyling bin is full, then they move good recyclables from my recycling bin to my trash bin in order to try to find cans and bottles. Often, then don't move them back when they're done rummaging.
Yeah, in theory I have 0 problem with people picking through the dumpsters at my place. In practice though trash gets thrown around outside the dumpster for the wind to make a mess of the parking lot with. I wouldn't care at all if they would just pick up after themselves. But they don't - so I do care.
So why not provide a bin for them for the deposit recyclables? I'll tell you what, if you would like to pick out your preferred bin, show me it, and I'll pay for it for you. If that's really your problem then I can make the effort with a simple and easy solution.