That was my first thought too! So many things in old-english are very very close to modern German, so it's sometimes surprising to see these false-friends.
Based on the page you linked, they pretty clearly are false friends: Old English unc is unrelated to modern German uns, it is related instead to Old Germanic unk (while modern German uns is just Old Germanic uns).
I think this is straining the meaning of false friends. They are derived from closely related forms and differ only slightly in meaning: "to us two" versus "to us all". I guess if you see that as a significant difference, but a more typical example would be English parents vuersus Italian parenti meaning kin.
I would argue that parents / parenti are also closely related meanings and closely related forms (and Italian parenti ultimately derives from the exact same root as English parents, the Latin parens meaning either parents or more generally ancestors). In contrast, uns and unc derive from separate PIE roots, while the semantic distinction was important in both PIE and Old Germanic.
Edit: Check out the Proto-Germanic personal pronouns.
https://en.wikipedia.org/wiki/Template:Proto-Germanic_person...