That's what I've been saying since forever...
When I have to spend time cleaning up my own drafting like this, I need to focus on the other stuff I am trying to do--although your addition of the bold in my quote is what raises the issue.
Even though there is no legal marriage record (a license; a certificate; a pastor's report; whatever), I think there is enough record to make them legally married for most purposes; for property ownership purposes; for purposes of testing the legitimacy of their children; for joint tax return filing; for a whole host of other legal issues in most jurisdictions involving the question of marriage even though there isn't any civil authority record.
To determine whether they were or were not married for any specific purpose, you would have to look at the law on that particular purpose and at local marriage law.