Is there a functional difference between contrived or convenient versus revealed?
Fictional works have a long history of revealing solutions at the high point of tension, where they best serve the drama.
Usually with some degree of foreshadowing, though, or they do indeed feel contrived or convenient. If a solution is revealed that makes sense given what we know about either the world or the timeline of the story, it can feel natural instead of contrived even with a reveal.
The caveat to this being when Deus Ex Machina was not only common but praised, such as ancient Greek plays. Which only goes to show that asking the question "What is the point of this story?" goes a long way towards establishing the proper expectations for plot development, which include willingness to accept scientific contrivances.
After all, I don't hear many people scoffing at Iron Man's manueverability considering the strength of his rocket propulsion system, or asking how Angel can bone Buffy even though he doesn't pump blood through his body (being dead and all).