Wait, aren't those two statements opposed to each other?

Different versions of a paper should have different DOIs. A DOI is fundamentally quite abstract, and there is no reason that an object-appropriate versioning scheme can't be laid on top. Figshare, for example, uses a versioning system where there is a single DOI referring to the overall artefact (e.g. 10.6084/m9.figshare.2066037) and a versioned-by-suffix DOI referring to a specific version (e.g. 10.6084/m9.figshare.2066037.v16). That works really well IMO.