I don't know about the US, but that's definitely true here in Canada.
One year I made a few bucks working as a "Christmas casual" at a mail sorting plant. In our orientation, we were told that if we happened to handle a card or letter which was addressed to us, and took it home instead of passing it through the system, we'd be fired on the spot, and perhaps charged with theft. Same if we found a letter we ourselves had written, but had changed our minds about wanting to send. The mail is the property of Canada Post from the minute it's dropped into a mailbox until the minute it's delivered to your house.
As for garbage, the Supreme Court of Canada has just ruled that you have no right to private garbage:
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"The Supreme Court of Canada has dismissed an appeal from a convicted
ecstasy trafficker who argued police violated his privacy rights by
searching through his trash.
"In a 7-0 ruling issued Thursday, the court said Russell Stephen
Patrick had abandoned his privacy rights when he put the garbage bags
out for collection on the edge of his property behind his house.
"The bags were unprotected and within easy reach of anyone walking
by in the public alleyway, including street people, bottle pickers,
urban foragers, nosey neighbours and mischievous children, not to
mention dogs and assorted wildlife, as well as the garbage collectors
and the police," wrote the court."