It's perfectly correct to use just an apostrophe as a possessive in a name ending in -s; "We are Daenerys' brothers" should have been accepted without the typo remark.
Technically true, but also quite poor form.
The main reason being pronunciation. In all cases of names that end in "s", you must pronounce the possesive with an extra sound /z/. However in any other word that ends in s, like a plural, you don't pronounce an extra sound.
John's. Pronounced as written.
Schools'. Pronounced as written.
James's. Pronounced as written.
James'. Pronounced as James's.
It is still grammatically correct, but as a native English speaker it seems so wrong.