Great discussion.
Yes, both of these are correct. Common names don’t need to come from a recognized authority, but they should be in common use somewhere. Common names on iNat serve mainly a utilitarian purpose - so that someone familiar with a common name like “stinkpot” (love it) can select the correct taxon when making an ID.
While I agree that common names are great for helping people engage with and remember taxa, iNat (and I just did a quick straw poll with the team) asks that only names which are already commonly in use be added, per the current guidelines.