I'm pretty sure that's not true. IIRC there is nothing you can do to completely eliminate Remnants from a system, even the Low Risk ones.
I am pretty sure it is true. I did it several times. All you need is destroy the nexus. There are no need to destroy fleets he spawn - they will disappear in few month (or years

). Only several initially generated (usually weak and dormant) fleets will remain after that. Kill them and that it - system is clear.
Sometimes people think remnants are respawning even in low-threat systems, because they sometimes patrol around outer reach objects, so player have not kill them, "cleaning" the system. And when you came back again - those patrols already guard another objects.
Also, I hear some mods make [REDACTED] respawn. But it not happen in vanilla. Unfortunately.