I don't live in Orange Park or Florida. Where I live, construction debris goes to a separate dumpster if it's a huge amount. The homeowner just munches up what they can and puts it into the dumpster.
It depends on the size of the project. To remove a window, you are going to have a lot of garbage that wouldn't fit into a garbage can no matter how much you tried to much it, so you would have to bring it to a dump and pay to have it disposed.
We no longer have a landfill where I live, but the homeowner or whomever, drives to the former landfill and can pay to dispose of tires, frigs, whatever. Just what was listed like on the Chesser landfill I believe. NO ONE can sneak in. They have guys there looking at every load and telling you where to put the different stuff in your load. The people there also have free piles for stuff that others can dig through and I think the people that work there take the good stuff.
It's a lenghty answer, but if you are asking can someone throw construction materials inito the garbage. Yes. No problem.
The other thing that is different from where I live is that we pay for our garbage and it is not attached to anything.
In OP the garbage is paid on an electric bill if IIRC, so no one would notice or care about someone putting something into a dumpster.
Here people are much more aware because we all pay by volume. The greater the volume, the more you pay.