IIRC, formally "personne" has to be used with the "ne" negation in order to mean 'nobody', such as "personne ne l'a vu", which makes a certain kind of sense ('a person hasn't seen it' -> nobody has seen it). But French people usually drop "ne" in spoken language.
You're right as far as I know.
But it's also funny to type in both "nobody" and "anybody" into Google translate and they both translate to "personne".
“Sans personne” means “without anyone” and has no “ne”.
Ok, but it literally means "without person", so is equally unsuprising.
And "rien" (nothing) used to mean something (via latin "res")
"Un petit rien" => a small thing
Typically used in "les petits riens de la vie", meaning the small things in life that may be overlooked but constitute the true things that make it worth living.
Personne on its own means ''no one'', but une personne means a person.