Modern language simply.
And I say that, with the idea that I've only ever heard "by some divine miracle", which completely suggests "by god" but is a more appropriate use.
And that would be because people have begun calling many things 'miracles', so the term miracle has completely lost its importance in divinity, so they say 'divine miracle' to clear that up.
People that refer to anything as a miracle these days tend to use it to just describe something completely against all common beliefs. Say, a sports game where someone was basically, by basic stats of the team, supposed to win/lose by a large margin, but turn around and do what nobody expected.
Now, the highly religious tend to keep the term miracle to being only in terms of divinity, but the term has become readily accepted in non-religious conversation.