You would be correct if you tossed your crammed container from a moving car in the dead of night. But maybe not otherwise.
I said "interesting" because there's some ambivalence in the courts. While it is true the authorities can search without a warrant that which has been abandoned, if the (municipal) government requires you to put your trash in a can or bag and place your trash in a certain location, that's not the same as "abandoning."
If, then, the cops can go through your stuff, their rummaging is the equivalent of a 5th Amendment violation - you are being required to incriminate yourself. An incriminating document in a city-mandated trash bag is exactly the same as being in a safe in your home. The cops have to get a warrant. Or so the 9th Circuit has ruled.
On the other hand, if the person doing the scavenging is not affiliated with the government, say a reporter or private detective, you have a whole 'nother matter. Again, if the city requires you to surrender your wet nasties to the city, then the reporter or private eye is STEALING from either you or the city and is, as my Indian neighbor says, in "heap big trouble."