To my mind, the answer is simple: Yes, Indexes are changes and should be governed by change control.
Indexes have a cost (not least disk space)
Indexes can have negative as well as positive impact on performance, as mentioned in the article
Index changes DO need to go through non-functional (and functional) testing
Indexes are part of the database schema and should therefore be stored in source/version control like everything else, not added ad-hoc by anyone.

Closer ties between dev & ops is certainly worth aspiring to, i.e. "devops" if your organisation is suited to it.