> When was the last time a major distribution found a backdoor in a popular package?
Packagers not finding a backdoor doesn't mean that there isn't one. How many packagers actively audit the code they support for a given distro? It is not uncommon for distros that support esoteric platforms will claim a given package works for that platform because it compiles, but it reliably segfaults on execution. Who's responsible for that? Packagers have even introduced[1] vulnerabilities by "fixing" code they didn't fully understand at the time.
Packagers have a difficult, thankless task, and we're doing them no favors by being confused at what their job is. They ensure that the package builds, integrates with the rest of the distribution as much as possible and updates/patches swiftly when issues are found upstream.