It seems to me that the sort of faux deus ex machina described in the question is perfectly acceptable. As to whether it works for readers, or is sufficiently foreshadowed, that requires reading the whole work, and is a question for the author's beta readers.
But then, I don't agree that a true deus ex machina is always bad for the story; it often is. But it can be part of a good story. An essential part, indeed.
For example, consider The African Queen by C. S. Forrester. (The book, not the movie based on it.) In this book, the central problem, to which the two MCs are dedicated for most of the narrative, is the destruction of the German gunboat Louisa, which gives the German forces total control of the river and lake. Their plan for this destruction fails totally, and the Germans are about to hang Charlie as a spy when Rose is rescued. Unwilling to hang a European woman, the German Captain of the Louisa sets them both on shore at a British outpost on the lake. From this same outpost, a few days later, an armed British speedboat sets forth after the Louisa. Having longer ranged guns, and twice the speed of the Louisa, it easily sinks her.
Neither the characters nor the reader had any idea that the British speedboat existed until after Charlie and Rose were set down at the British outpost. It is a pure deus ex machina. It solves the story problem with no effort by the MCs and would have done so in exactly the same way had they both fallen dead on page 10 of the book. Their efforts are totally irrelevant to the outcome.
The real story problem, unknown to the characters, is their character development, and the real climax is the scene in the gorge, where Charlie, at the insistence of Rose that they do not simply give up, repairs the damaged propeller, a task had considered far beyond his powers, and the two become lovers. Rose has learned to be less puritanical and convention-bound. Charlie has learned a sense of self-discipline and confidence. The remainder of the book develops these qualities further and displays them in action. The point is the value of the human spirit and the best efforts in the face of adversity, even if no result is achieved or no one ever knows of the efforts, much the same point as is made in the author's Brown on Resolution
In the movie version, the swamped African Queen destroys the Louisa using the improvised torpedoes that Charlie created at Rose's insistence, thus making their efforts successful, albeit only through an enormous stroke of luck. This removes the deus ex machina but reduces the emphasis on the character development, thus in my view weakening the story, not strengthening it.
Thus I say that in a rare case, a true deus ex machina can actually strengthen a story, by revealing that the apparent story problem wasn't the true issue at all.