Do you feel the same way about putting your trash in bins (or even bags), as opposed to leaving individual items strewn about your lawn for them to pick up? Do you feel the same way about getting your car to the mechanic instead of having him pick it up from wherever you left it?

The line you're drawing to define "labor done on behalf of a paid service provider" is laughably ridiculous. The service they provide is "picking up sorted bins of trash". You're not "doing their work for them" to meet the terms of the paid service agreement.