This isn't how I'd describe the guarantees provided by a package manager. In fact, most package managers don't really provide any guarantees at all; almost all of them support something like preinst.sh and postinst.sh scripts which can basically do anything. It's the package
maintainers that are supposed to provide the guarantees you describe. Of course, they're only human, and their incentives might not line up with yours.
And if you stray outside the official channels, as most users must at least some of the time, then you're back to all-bets-are-off. Fetching and installing packages from a channel hosted by some third party really is no better from a security standpoint than running a (signed) shell script from that same party.
EDIT: I should add that there may be some new, advanced package management systems that do actually provide strong guarantees, like only putting files in certain directories, never setting the setuid/setgid bits on executable files, or perhaps ensuring that all files from a package are owned by a user:group associated with that package (the Linux From Scratch docs describe a package management scheme like that, it's worth checking out). I'm referring here to the majority of popular package managers, e.g. dpkg, which will run arbitrary code during installation.